Substitute Anthony Martial gave the hosts the lead with a fine curling effort but Joe Allen levelled for the Potters in the 83rd minute.
But Mourinho is convinced his side gave everything they could in the 90 minutes and that on another day it could have been 6-0.
He said: “Best United performance all season. It could have been 3-0 or 4-0 at half time, 6-0 at the end of the game, but the result was 1-1. But that’s football.
“It was a much better performance than against Leicester. It was the best performance by far, six, seven, eight great chances to win the game.