Cole dismissed any suggestion United could struggle to get over the agonising manner in which they surrendered the English league crown to neighbours Manchester City.
Manager Sir Alex Ferguson claimed before the epic final day of the season a fortnight ago that City might suffer "untold" damage were they to blow their chance to win a first title since 1968.
Cole insisted United were made of stronger stuff, having almost always bounced back from failing to retain the Premier League by regaining it the following season.
The former England striker was part of the side that famously did so in 1996, having blown it on the final day of the previous campaign in similar circumstances.
"I see that in whatever Manchester United team there is," said Cole at this weekend's British Airways Football Legends Invitational Tournament in Barbados. "No-one wants to lose, especially last day of the season.
"You can't wait for pre-season to come around because you want to get the season started again.
"I would imagine that next season the boys will come back much stronger, determined to try to win the Premier League again."
Cole, now an official ambassador for United, backed Ferguson to ensure they would not take this season's outcome lying down.
He added: "The gaffer's very, very disappointed that we lost it the way we did do but, ultimately, he brushes it all underneath the carpet and says, 'Hey, it's gone now - let's look towards next season'. He always does that.
"He'll bring in new players, everyone knows that, and he'll have a right good go at it again.
"Because that's what the manager is. He loves a challenge.
"He said that when we won our 19th championship, he said that last season, that we love a challenge and whoever throws down the gauntlet, we're prepared to challenge them.
"Man City have done that now and, no doubt, are going to be a challenger."
Having lost the title on goal difference, Cole envisaged Ferguson strengthening in midfield and up front in particular.
"He's let a centre-forward go in Michael Owen, so he might look in a centre-forward position," Cole said. "He's been linked with a couple of midfield players as well, so we'll just have to wait and see."
Cole insisted his former team-mates Ryan Giggs and Paul Scholes could also be huge assets next season, despite being 38 and 37 respectively.
"The two of them, again, last season were absolutely fantastic," he said.
"For their age, the way that they played was unbelievable.
"We've been linked with a couple of players in that midfield area.
"If you use Scholesy and he plays 20-25 games, what a 25 games he'll give you, because he's a phenomenal player.
"If Giggsy plays 25 games, he'll give you a fantastic 25 games as well.
"If he (Ferguson) looks to bring in new players - no doubt he will do - to have those married in with Scholesy and Giggsy, it's going to be absolutely fantastic."
However, Cole warned City would hardly be resting on their laurels themselves this summer.
He said: "If you've got those kinds of financial resources, naturally you're going to buy a few more players to make you're team stronger.
"Just like they're going to strengthen, Man United will look to strengthen, Chelsea will look to strengthen, and so will Arsenal.
"So, you look at those big four.
"You can't count Tottenham out. They'll look to strengthen as well.
"All of those teams next season are going to believe that they can win the Premier League."
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