United suffered another semi-final setback at Old Trafford, with second-half goals from John Stones and Fernandinho ensuring City will meet Tottenham in the Wembley showpiece on April 25.
Solskjaer’s men were dumped out of all three cup competitions at the same stage last season, meaning their torrid run in the last four has continued.
After the City defeat, Pogba appeared to aim a subtle dig at Solskjaer over his setup on the night, insisting it was “details and set-pieces” which cost United.
The France midfielder said: “It is about details. Details make the difference all of the time and now when it is big games like this, it is details and at set-pieces we lost [from].
“We have to learn because it is not the first time. We have to learn.
“We have to get through this as well. Then after this there is big games coming up so after tonight we go again.”
United were also beaten by City in the Carabao Cup semi-finals last season, coming before further last-four exits at the hands of Chelsea and Sevilla in the FA Cup and Europa League respectively.
Pogba admits it is a major disappointment to have missed out on another cup final, while issuing a rallying cry to his team-mates to “do better” in the future.
“Of course [it is disappointing] because it's not the first one as well against City at home,” he added.
“We are disappointed with the result, obviously, with the two goals from set-pieces. And after you know it can go both ways. We lost today and it's not the first one, like I said.
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“It's very annoying to lose because there's always a trophy behind all of this and we have to do better. We have to do better for sure.”
United now turn their attention to the FA Cup, with Championship outfit Watford due to visit Old Trafford in the third round of the competition on Saturday.