The Red Devils, including manager Mourinho, were under pressure after losing to Tottenham at home last weekend. Despite the loss, a section of fans stayed after the final whistle to salute Mourinho and his players.
They were rewarded on Sunday, with two first-half goals from Romelu Lukaku at Turf Moor enough for United to seal all three points and push themselves back up to tenth place on the Premier League table.
"The quality of the performance and the happiness within the team is Old Trafford's responsibility," Mourinho said.
"The reaction after the game at Tottenham was fundamental to keep the team moving in the right direction."
He added: "In the first 10 minutes we played so well that it reminded me of the Tottenham game because we were dominating opponents - but this time we scored.
"Should we score six, seven and eight? Yes we should.
"But at least we scored two and the team was strong, defensively very good. Even with 10 men we were the team that had chances to score. We are very happy the boys can go on their international break with the feeling of a good result."