Jurgen Klopp sarcastically congratulated a TV journalist on James Milner's injury and called Sheffield United boss Chris Wilder "selfish" in another spiky post-match interview.
The Liverpool manager was talking to BT Sport after his side's 1-1 Premier League draw at Brighton.
"I don't know how often I have to say it. You picked the 12:30," he said to reporter Des Kelly.
"After Wednesday, Saturday at 12:30 is really dangerous for the players."
Klopp had previously warned that playing games on Wednesday and then being involved in the early Saturday match would cause problems.
"Until this year is over in this part of the season we had this slot three times," he said. "Look who else had this slot three times? No-one."
Everton - who are not in Europe - will have played the Saturday lunchtime slot four times by the end of the year, with Manchester United - who are in the Champions League with Liverpool - also playing three.
|Teams to play Saturday 12:30 games this season after Wednesday matches (including December fixtures)|
|2: Liverpool (28 Nov after Champions League, 19 Dec after Premier League)||1: Everton (19 Sep after Carabao Cup)|
|2: Man Utd (7 Nov after Champions League, 26 Dec after Carabao Cup)||1: West Brom (19 Sep after Carabao Cup)|
|1: Man City (24 Oct after Champions League)||1: Brighton (26 Sep after Carabao Cup)|
Liverpool lost 2-0 to Atalanta in the Champions League on Wednesday after resting several first-team regulars.
Three teams have played on Saturday at 12:30 after a Wednesday Champions League match - Manchester City, Manchester United and Liverpool, once each.
Tottenham have played a Sunday 12:00 game after a Thursday night Europa League match, which is a similar turnaround.
Liverpool's other 12:30 Saturday game this season - a 2-2 draw with Everton - came directly after an international break.
They have another one next month when they play title rivals Tottenham on Wednesday, 16 December before facing Crystal Palace in the early Saturday slot.
"Why did you pick us against Crystal Palace if you care?" Klopp said to Kelly and added "congratulations" when asked about a hamstring injury to Milner.
Klopp made similar complaints to Sky Sports after a 3-0 win over Leicester last week and Kelly pointed out that Premier League clubs have agreed to the schedules.
Klopp said: "We have one more Wednesday and Saturday 12:30 before new year. These are difficult moments. If you play at 15:00 or 17:30 it's exactly the same [from a TV point of view]. I'm not having a go at the broadcasters, I'm just saying how it is.
"It's not only my players who have that problem. I only go for the broadcasters with the Wednesday to Saturday at 12:30. Seven other managers [in charge of teams in European competition] have the same problem."
Klopp also spoke again about the need for Premier League teams to be allowed to make five substitutions - as they can in other countries and the Football League - and was very critical of Wilder.
"Ask Chris Wilder how we can avoid that [injuries]," he said.
"We had a talk between managers - a week ago now, I think - it was 15-5 if not 16-4 for five subs.
"Chris Wilder says constantly that I'm selfish. I think the things he's said shows that he's selfish. I was in a similar position at Mainz, all about staying in the league.
"Today, if we had five subs, I take off Andy Robertson and bring on Konstantinos Tsimikas. To save Robbo. Not to make our game better, just to save him. It's not about changing tactics and systems, it's just to save the players."
Wilder, speaking to Sky Sports after Sheffield United's 1-0 loss at West Brom, said: "There are 20 votes in this league and everyone looks after themselves.
"I've got a huge amount of respect for Liverpool and Jurgen. Whether it's looking after the club or it's selfish… There are a few other managers who have looked after their own and I will always look after Sheffield United."
Klopp appeared to regret his BT interview when he spoke to BBC Sport afterwards.
"From time to time I try to mention a few things which are a problem but not now because… oh I did it already because he wanted to have that interview and we had it," he told Match of the Day.
"It's silly enough to fall into that trap and now he has the headlines he wanted."
The German reiterated that he thought "Wednesday, Saturday is completely normal" and his only grievance was the lunchtime slot.
"This world is ruled by other people, the Premier League by Chris Wilder because he can decide all of us don't need five subs because he doesn't," he said.
"We had the meeting. Everyone had to speak. Chris was clear, he thinks it's not helpful for Sheffield United so doesn't want to change. Fifteen others, if not 16, said they wanted to change.
"That would be enough if there was a vote but since then nothing happened. If that happens in January it could be too late. There are a lot of games to play."
Henderson would like VAR scrapped
Liverpool, who went top of the Premier League with the point, had goals by Mohamed Salah and Sadio Mane disallowed for offside by the video assistant referee.
They led through Diogo Jota's goal but conceded an injury-time penalty - also a VAR decision - after Robertson tried to clear the ball but kicked Danny Welbeck's foot instead.
Pascal Gross scored the penalty to equalise, after Neal Maupay had missed a first-half spot-kick.
"I can't really speak about it because I'll get myself in trouble," Reds captain Jordan Henderson told BBC Sport.
"If they're offside, you do the line thing, then what can you do? The third one, I don't know, it's not a penalty. You can think I'm biased but if you ask four or five of their lads they will say the same thing.
"They said it walking off the pitch. You feel as though there are a lot of decisions that go against you but that decision for me today is baffling.
"I don't want to speak for anybody else but in my opinion I would [scrap VAR]. I just want to play football as normal."
Klopp said the offside decisions were correct, although "it was tight".
He added: "We are used to armpit offsides against us. The first penalty I heard was a penalty, the second one we can all make our own decision.
"The second one, my decision is the referee gives it, it's a penalty. There's contact. If he decides it's enough… usually a good ref sees when players on the other team say 'nah, that's not a penalty'. And they said it'."
- Watch 13 FA Cup second-round games on BBC iPlayer, the BBC Sport website and app this weekend. Find out more here.