The Red Devils held Arsenal to a 2-2 draw at Old Trafford on Wednesday night.
Arsenal led twice, however, United fought back to secure a crucial point in the race to finish in the top four.
Mourinho has cut a frustrated figure this season after a below-par summer transfer window.
The United boss desperately wanted a new centre-half, however, Red Devils executive vice-chairman Woodward refused to back his manager.
And following the Arsenal draw, Mourinho couldn’t help but fire another dig at Woodward.
“We shoot ourselves so many times during the season. That is really difficult,” Mourinho told BT Sport.
“Big soul by the players, fantastic attitude from the first minute.
“Many players in difficulties, some good performances, some players in difficulty.
“Diogo Dalot the first start, Marcos Rojo the first minutes, Matteo Darmian the third start, Eric Bailly doesn’t play for a couple of months, Chris Smalling, a brave guy to play with such difficulties – the boys left their souls.
“And when sometimes people speak about quality… [sighs].
“We should win game we made two big mistakes for their goals.
“We made other mistakes that allowed them to have counter attack situations, easy passes that we lost, easy controls that we lost, things that at high level normally you don’t do it.
“Our performance is marked by these ups and downs.
“The second goal comes in awful moment for a team that was on top of the game.”
When asked if it’s positive the United players are sacrificing themselves, Mourinho added: “Yes, positive but there are things that I cannot get from them and I cannot say much more than this.
“Big soul, everybody gives everything, that is for sure and that’s a positive feeling.
“I cannot tell you much more I prefer just to say I’m happy with soul commitment bravery I’m really happy with that.”
United are back in action on Saturday afternoon against Fulham.