Manchester United needed a Marcus Rashford goal from the bench to settle the nerves against the Foxes.
Leicester defended valiantly and Kasper Schmeichel saved Romelu Lukaku’s penalty to frustrate the Red Devils.
But Rashford’s goal and another from Marouane Fellaini secured the win.
“That’s why need them, because they can change the game. We’re happy for them,” said Pogba.
“Is that a game that we might not have won last season? Yes, for sure.
“I was a bit scared but we keep pushing this season.”
Rashford was the impact man, coming on to score 20 minuets from time.
And the England striker was pleased to get the win.
“We created a lot of chances in the first half and it seemed like it was going to be one of those days,” he said.
“But the team stuck to the task and thankfully we got the goal.
“When the chances are coming then I’m confident of getting the goals.”