The Foxes brought United's record away run to a crashing end as Ole Gunnar Solskjaer's men collapsed during a chaotic end to a thrilling clash.
Both sides were looking to return from the international break with a bang after recent struggles, with the visitors higher in the Premier League but under more intense scrutiny.
That focus will only increase after Leicester won 4-2 at a rocking King Power Stadium, where Jamie Vardy and substitute Patson Daka scored late to condemn United to a first away league defeat since January 2020.
Pogba endured a difficult afternoon in the midlands, with Youri Tielemans and James Maddison controlling proceedings in midfield, effectively nullifying the World Cup winner.
Speaking in his post-match interview, Pogba admitted the Red Devils deserved to lose the game and accepted there would be pressure from the supporters.
"To be honest, we've been having those kind of games for a long time," Pogba said.
"We haven't found the problem. To concede goals, easy goals, stupid goals… the fans are going to push and put pressure on us.
"We need to be more mature I think. We need to play with more experience and arrogance, in a good way.
"We have to take the ball and play our football. Now we have to find what the key to this change is. I think we deserved to lose today."
United were knocked out of the Carabao Cup before the international break, also dropping points at home to Everton and Aston Villa, while also struggling in the Champions League.
Manager Ole Gunnar Solskjaer is under intense pressure and could well be staring down the proverbial barrel next weekend after games against Atalanta and Liverpool.
And the former Juventus midfielder insists a shift in mindset is needed if they are to sustain a challenge on Premier League champions Manchester City.
"It's all of us. We need to find something," Pogba added. "We need to change something. We really don't know.
"It's frustrating because it's something we don't understand, but we have to find out very fast to compete.
"If you want to win the title, it's those games you have to win - even though they're very hard, even though we're playing away. We need to find the right mentality, the right tactic, to win those games.
"We will have time to think about it, and we have to stick together and find the problem."