Dimitar Berbatov, the former United striker, believes it is time Mourinho and Pogba settled their differences.
"I am the manager I make these decisions, no fall out at all, no problem at all", says the Manchester United manager.
"A great player and a World Cup victor, but poison".
Woodward has also come under fire after overseeing a summer transfer window during which United spent £68m to sign Fred, Diogo Dalot and Lee Grant.
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.
Pogba still turned up at Old Trafford, watching from a private box, but disappeared before the shoot-out.
"I've said it before, and I'll say it again, there are too many at Manchester United prepared to hide behind the flak that Jose Mourinho is taking for his style of play".More news: Trump gives news conference in New York City
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And Pogba's absence from Tuesday evening's squad appears to confirm the breakdown in relationship.
But while there is a sense of exasperation with Mourinho's approach, there is also an air of helplessness among the players due to the realisation that the club remains supportive of the manager.
"We are proud that, once again, last season we had more academy graduate minutes on the pitch than any other Premier League club".
United face West Ham at the weekend, and fans want to see Pogba back in the starting line-up.
Manchester United, now seventh on the Premier League table, also went on to play an 1-1 draw against Wolves at home on Saturday.
Mourinho and Pogba have been engaged in a stand-off for some time now after the Red Devils boss hooked the Frenchman in a defeat by Tottenham in January.
Derby defeated United 8-7 on penalties at Old Trafford after the third-round clash ended 2-2 at 90 minutes.
When Jose Mourinho joined forces with Paul Pogba two years ago, the marriage of a great manager and the world's most expensive player was hailed as the partnership that could reignite the fire in an ailing Manchester United.