The Frenchman, who is out of contract next summer, is being linked with a move to Paris Saint-Germain this summer.
Pogba, whose talent has never been in question, has not always endeared himself to the United faithful with the comments of his agent and his inconsistent performances.
However, Cole has little patience for critics of Pogba.
"People expect too much from Paul Pogba and the criticism he gets is unfair," Cole told independent.ie.
"I'm one of his biggest fans and I think he is world-class, without a doubt, but when he has a bad game or doesn't play at his best for a few weeks, everyone is on him.
"Maybe he hasn't always been played in the right position at United because you look at how he played when he was at Juventus. And when he's in the France team, he looks fantastic.
"The disappointment for him at United has been that he came back to try and push the team closer to winning the Premier League title again, and that hasn't happened.
"Whether he stays at United for next season remains to be seen. Maybe the decision has already been made, but I think it will be a shame if he leaves and doesn't achieve what he set out to do at United."