A day after Woodward failed to deliver the centre back that the manager desperately wanted, Mourinho laid bare his frustrations with United's executive vice-chairman, claiming that teams will no longer fear playing them if they do not spend more.
In recent weeks, Pogba has been linked with a move to Barcelona and his relationship with manager Jose Mourinho has appeared strained, especially after the player didn't return to preseason training early like many of his team-mates.
"We should start the Premier League with a win and we did", he said.
"We have to wait until the end of November to understand if we can fight for the title", he said.
After sealing deals for Fred, Diogo Dalot and Lee Grant by early July, last season's Premier League runners-up were unable to add further despite the Portuguese's explicit desire to bring in two more players. "We must get used to teams who have players of the same quality that we have", he said.
United were not convincing as Leicester displayed wonderful creativity and had good possession throughout the first 45 minutes of the much-anticipated match.
'Of course, we have second or third choice in case he is not confident or for some reason doesn't want to take it.
Pogba confirmed that it was his decision to take the penalty ahead of Sanchez from the group nominated by Mourinho. "Pre-season was very hard and we needed this fantastic spirit by the players to manage this performance and this result". I know it's a great cup, it will stay in my mind, but I want to win all the trophies.
"The target is the Leicester match", said the United manager.
Pogba was a monster. "Even if I forget the goal, it was a complete performance", said Mourinho of the left-back's display.
But considering Victor Lindelof and Eric Bailly had played so little together in their time at United - just 99 minutes in total before Friday's game - they looked pretty solid and sturdy at the back.