Rose, who is on loan at Sunderland from Tottenham, was sent off after the final whistle for kicking the ball away in reaction to the abuse he was receiving.
His father added: "It's quite clear they [Serbia's fans] are making monkey chants.
"Dan's only possibly being singled out because of the red card but there were other black players out there and no doubt they were being racially abused as well.
On the red card, he continued: "It's like a smack in the face. It's a joke. He kicked the ball in anger because of what went off and the referee has given him a red card.
"Hopefully the red card will get rescinded. The powers that be will look at that and say that he kicked the ball in frustration and the referee shouldn't have sent him off.
"Only one red card came out and that was for kicking the ball. Even [England U21 manager] Stuart Pearce's number two [Steve Wigley], the way they assaulted him is unreal.
"I can't believe in this day and age that's actually happened. It's like a bad dream gone wrong."
Racist chanting mars England U21 match. This footage may contain offensive language.
When asked for his reaction following England's 1-1 draw in Poland on Wednesday, captain Steven Gerrard told BBC Sport: "The disappointing thing is that we seem to be back to square one.
"Lots of people above me need to take control of this situation and sort it out once and for all.
"No-one else can do anything about it except the authorities. They are the people in control. They are the people who can ban people and give massive fines out so it won't happen again. Why wait? Do it now."
Serbia midfielder Nikola Ninkovic, who played in the match, has conceded that he was wrong to push Rose in the incident but claims the England player was the instigator.
"The guy three or four times made inappropriate gestures towards our fans," Ninkovic told Serbian newspaper Novosti.
"I was angered by his reaction so I rushed over to explain to him that he should not do that.
"I did not mean to hit him or insult him. I walked over to him and pushed him.
England U21 win over Serbia U21 marred by brawl
"A lot of his behaviour annoyed me but I know I was wrong and I know I will get a fine.
"He received a red card and I got a yellow. That is probably an indication that his share of the story was significant."
The Serbia FA has been charged with alleged racist chanting by fans and both associations over the behaviour of players at the end of the game.
However, the Serbia FA released a statement on Wednesday saying a connection between the on-pitch scuffles and racism had "absolutely no ground" and also blamed Rose for the clashes because of "inappropriate, unsportsmanlike and vulgar" behaviour.
On Thursday the country's football federation requested statements from all players and staff involved in Tuesday's U-21 international.
The FA has urged Uefa to take the "strongest possible action" against anyone found guilty of racism.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.