The Blues kicked off their league campaign with a comfortable victory at Turf Moor, scoring thrice in the first half after conceding the opener to the promoted hosts.
Scott Arfield fired Burnley ahead in the 14th minute but Chelsea's response was emphatic - as they built a two-goal lead within 20 minutes of trailing.
Heralded signing Diego Costa equalised three minutes later, before Andre Schurrle made it 2-1 in the 21st minute and Branislav Ivanovic increased their buffer later in the half.
Mourinho said his players did not panic despite the early scare.
"I think we had a good reaction, and the first part of that reaction is the fact that emotionally we were not affected by the goal conceded," the Portuguese tactician said.
"We conceded the goal and kept playing according to the way we are training and to the way we want to play.
"The players were very calm.
"They never lost their composure, they never lost the footballing idea, and after that we had a fantastic 20-25 minutes with three goals - especially the second one was a fantastic goal, plus the penalty that the linesman decided not to give - and in the second half we had control of the game."
Mourinho conceded he was the most concerned person in the Chelsea camp, as he felt his players went into the season opener underdone.
"I know I was a bit afraid because I know my players are not in their top physical form to give the same kind of performance for 90 minutes, so we lost a little bit of attacking appetite," he said.
"But the control of the game and the control of the ball possession was always there and I think we clearly deserved these three points against a side that is going to give a fight to everyone that comes here."
