It appeared two points would be dropped by Mourinho's men as an entertaining contest looked likely to end goalless until Phil Jagielka was adjudged to have fouled Ramires in the left channel.
Frank Lampard's inswinging free-kick was glanced down by Branislav Ivanovic and captain John Terry, returning from a three-game absence with a gluteal muscle problem, slid in to score past Tim Howard.
"When you score minute 90-something you can speak about being lucky," Mourinho said.
"The reality is that the boys chased that. We were the team that was really trying to win, which is our responsibility.
"We deserved it. I never thought we would score so late. I had hope that we could score a goal before that. Destiny wanted last minute."
Everton boss Roberto Martinez was frustrated with referee Lee Probert's decision to award Ramires the free-kick.
The Spaniard suggested Chelsea were cute in winning set-pieces around the area.
"Ramires looks for the contact and if you watch the replay it's not a free-kick at all," Martinez said. "That happened with other incidents, four or five before that.
"It is very soft. (But) that happens in the game. I don't blame the referee at all.
"It's an incredible know-how, using every single trick in the book to get dangerous positions.
"We had to defend dead-ball situations well, but unfortunately in the 93rd minute they got a goal that I don't think reflects the performance.
"We defended really, really well. In that one, John Terry throws himself, brave and he gets the luck of the bounce and they score."
Mourinho had sympathy for Everton as it appeared Chelsea's winless run would be extended to three games.
Instead Chelsea stayed top of the standings entering Wednesday's Champions League last-16 clash at Galatasaray.
The Portuguese added: "I feel sorry for them (Everton) because maybe a point for them is fair after their good performance.
"If today we had only one point, if the teams that are behind us win we lose that position.
"Every victory keeps us there, every defeat or draw we lose a position.
"We just want to try to keep the position, not to give (it away) for free to the opponent.
"We have to fight, we have to play and it's a good feeling to win in the end.
"The team wanted to win. You score, it's fantastic. Even if you don't score my feeling would be a positive feeling with them. They tried everything."
Mourinho praised Cesar Azpilicueta's all-action performance as "representative of the desire the team put into the game" and bemoaned an injury to Oscar which brought the Brazil playmaker's afternoon to a premature end.
Oscar carried an undisclosed problem into the game and could be a doubt for Istanbul.
Mourinho said: "There was no risk to make it worse. He thought he could cope, but he couldn't."
Terry's return was a boost following the win over Newcastle, the draw at West Brom and FA Cup exit at Manchester City.
Mourinho added: "Again one great defensive performance by the whole team. It was not (just) John.
"The defensive organisation is good and strong, but when you captain, your voice, the stability, the complete understanding of him with (Gary) Cahill. I think it's good.
"He didn't play three matches and we clearly missed him."