The former deputy prime minister said so-called blue on blue assaults were “destroying the Tory party hopefully” but questioned “where’s Labour?” in the battle, the Press Association reports.
Remain campaigners could lose the June 23 vote because Labour is failing to secure backing from its supporters, he warned.
“It seems as if we are just enjoying the fight between them but that is not putting Labour’s position,” Lord Prescott told BBC One’s Sunday Politics.
“We are not putting Labour’s arguments.”
The peer said Labour was “absolutely” failing to galvanise its supporters, admitting “Jeremy’s not a passionate man”.
Corbyn has faced repeated criticism that his role in the campaign has been too low key.
In his second major intervention in the campaign, much of the Labour leader’s focus was on criticism of the Tories and areas where the EU needed to be improved.
Lord Prescott said Corbyn was right to refuse to share a platform with the Conservatives.
He said: “Don’t say, ah well, we all believe in Europe, let’s travel on the same bus. Nonsense. No wonder our people are confused.
“Get a strong Labour voice. I’m glad Jeremy’s said what he said but get putting out our case and point out what these beggers did in government.”
He added: “I do want to see a united party, we are not best at it at the moment,” he said.
Labour must set out more clearly where it stands on immigration, the peer added.
“Start saying where we stand and be a bit clearer on immigration. We have been cowards on immigration, not only Labour, the whole political establishment has avoided the argument.”
He added: “There’s going to be more migration coming from African countries like that, which have no water, no food because of climate change.”
The peer said global powers like the United States, China and India would set the course on issues like immigration, crime and security.
“We’ll just be a little island with a pea-shooter shouting out ‘don’t you recognise we are a big power’ but you’ll have no say in the decision.”
The peer branded Damian McBride as a “totally confused man” when pressed on claims the Labour aide has been giving advice to the Leave campaign.
Labour deputy leader Tom Watson admitted it has been difficult for the party to get its message across as media coverage has understandably focused on Tory Cabinet splits.
But he insisted Corbyn was getting a “raw deal”, saying he has been making several speeches for Remain.
Watson told the Murnaghan programme on Sky News: “It is quite hard for us to get our message across.
“When you’ve got the kind of battles that are going on across the Cabinet, we understand that, that’s the most newsworthy issue.
“It sometimes seems to me that the Leave camp is transforming itself into a Government in waiting and that is very hard for us to try and find the space to get our message over.”
He added: “I do feel very sorry for Jeremy though.
“He was in Cornwall campaigning yesterday, Cardiff the day before, he’s been making speech after speech after speech about Labour’s case to remain in the European Union and I think he’s getting a bit of a raw deal on that.”