Former United defender Gary Neville hit out at Woodward for not backing Mourinho in the summer, claiming Woodward should have "shown faith" in his manager and signed a centre-back, particularly after rewarding him with a new contract in January.
Which team are you supporting in the 2018 World Cup?
Pogba has widely been criticised for failing to produce consistent performances under Mourinho at Old Trafford, but he was in fine form as he helped France to win the World Cup in Russian Federation this summer.
Pogba helps lead France to the World Cup title, turning in a fantastic performance in the final, which included him scoring the eventual game-winning goal in a 4-2 win over Croatia.
Plenty of managers cite the need for their first choice players to rest but Lampard said the natural progress of the season will provide opportunities for most of his squad.
Manchester United have had a tough start to the season and this defeat will increase the pressure on Jose Mourinho.
"The players were happy with that decision and the reasons behind the manager's decision."
Asked if he could deny that Pogba had told Mourinho of his desire to leave United and join Barcelona, Mino Raiola, the player's agent, declined to answer yesterday.
"I think the World Cup is the flawless habitat for a player like him to give [their] best", Mourinho told ESPN FC.
On Monday, Pogba tried to downplay the issues with Mourinho, tweeting: "Some people make polemic even from "good morning" to create drama".
In the current situation he finds himself in, Pogba looks likely to force through a move away from Old Trafford and Premier League football.