The France international was handed his first Premier League start since a 4-2 defeat at Leicester City in the middle of October.
Pogba made his comeback from injury in Friday’s night FA Cup fourth round defeat against Championship club Middlesbrough and retained his place in Ralf Rangnick’s starting lineup at Turf Moor.
Pogba fired the Red Devils ahead just after the quarter-hour mark but his side had to settle for a point as Jay Rodriguez grabbed an equaliser for their hosts in the early-stages of the second-half.
The draw, coupled with West Ham United’s home win against Norwich City, saw Rangnick’s side slip out of the Champions League places - and Red Devils goalkeeper Schmeichel believes the performance was “not good enough” for the standards expect at Old Trafford.
“I said before the game Pogba played fantastic on Friday night. If Pogba plays like that we want to keep him, we desperately want to keep him,” Schmeichel told Premier League Productions.
“But he was completely out of the game today and you can’t have players doing that.
“That’s not good enough for Man Utd. At Man Utd you’ve got to have a very, very high low-level and at a minimum you’ve got to perform to that.
“You’ve got to have this type of urgency and understanding of when you need to push forward to get the goal you need.
“In the last 20 minutes, the way Man Utd played was all in the same tempo and all in the same pattern.
“There were no pressure balls into Burnley’s box, there were no questions being asked.”