The Red Devils lost the first leg of their quarter-final tie against the Spanish champions after an uninspired performance at Old Trafford, with a Luke Shaw own goal ultimately deciding the match.
Ole Gunnar Solskjaer's men were unable to carve out any clear cut chances in the match and failed to register a single shot on target over the course of the 90 minutes.
United are in the middle of a barren run across all competitions, with four defeats from their last five games and they have another mountain to climb at Camp Nou next Tuesday.
Pogba was unable to influence proceedings in any meaningful way against Barca and Ince says he failed to live up to expectations on the biggest stage.
The ex-United midfielder, who played for the club between 1989 and 1995, also highlighted the ineffectual efforts of Romelu Lukaku and questioned his role in the final third of the pitch.
"On the night, you’re looking at the so-called big players like Paul Pogba, Marcus Rashford and Romelu Lukaku to make something happen," Ince told Paddy Power News.
"You look at those to get the team going – and it didn’t materialise.
"Another off day for Pogba, which I didn’t expect considering how he’s been playing and Lukaku once again looked incapable of scoring a goal.
"He spent most of his time out on the wing, he just needs to play between the two goal posts.
"What use is Lukaku out on the wing? It doesn’t make sense to me. Anthony Martial came on and had zero impact.
"These are the kinds of players you look to change the game in such an important match, and it’s disappointing they couldn’t."
There were a few positives for Solskjaer to take from his side's performance, however, such as the work of centre-back pairing Chris Smalling and Victor Lindelof, who kept Lionel Messi and company quiet for the majority of the night.
Scott McTominay also produced perhaps his finest display yet in the famous red shirt, but Ince was surprised by United's conservative approach in such an important fixture.
"I would say that defensively they looked good, and Scott McTominay was brilliant, he was assured and comfortable and looked ready for the occasion," he added.
"He relished in that position and was easily the best United player on the pitch. He was a plus side of the game.
"But it was disappointing. They never had a go at Barcelona or tried to, in such a massive game where the fans are up for it. It’s a sad sight that at Old Trafford, in the Champions League, United aren’t having a shot on target.
"That Barcelona team were probably expecting a different performance from United. They’d have been expecting that resurgent Ole side who come at you from the off, that get in your faces, but that didn’t materialise."