Sunderland boss David Moyes accepted questions would be asked about his future after their "dire" performance in their 4-1 loss at Burnley.
The Black Cats end 2016 in the Premier League relegation zone after Burnley's Andre Gray scored a hat-trick and Ashley Barnes converted a penalty.
"It was a poor performance - really, really bad - and defensively we were all over the place," said Moyes.
"The players have to take responsibility as well as me."
He added: "You can ask me questions about myself and my future, that's fine. We're in the bottom three, I know that."
'Unless they back Moyes in the window, they will go down'
Former Newcastle striker Alan Shearer on BBC's Match of the Day: "Moyes was under pressure from the beginning of the season. He didn't have time to plan when he arrived late in the summer.
"There were a lot of rush signings. The chiefs told him he would have limited funds in January.
"Unless they back him in the transfer window they will go down."
'We made the same mistakes time and time again'
Jermain Defoe scored in the second half, but the result left Sunderland 18th in the table, with only one away win from 10 Premier League matches this season.
"We threatened at times going forward but we couldn't defend," added Moyes.
"We made the same mistakes time and time again; missed headers, missed bouncing balls, the same stuff.
"My players were well briefed on the opposition and you have to hope they take that into the game - but it was dire, as bad as anything I have been involved in here."
Sunderland already have injury problems and they increased on Saturday. Defender Lamine Kone went off after he clattered into an advertising hoarding and striker Victor Anichebe injured a hamstring at Turf Moor.
However, captain John O'Shea refused to make any excuses for his side.
"It was unacceptable, not good enough," said O'Shea. "Away from home you have to be resilient, but the goals we conceded were not acceptable and the players have to take responsibility.
"There is no excuse for what went on and it's something we will have to look at collectively and individually and dust ourselves down very quickly.
"The dressing room is not a good place but we know we can quickly turn this around. We have to have the attitude that we fight together."