The Londoners scrambled a win at Stamford Bridge thanks to a scrappy goal in the 93rd minute, captain John Terry sliding in to get the slightest of touches to a free kick out on the left from Frank Lampard.
The victory kept Chelsea F.C. top of the table with less than a third of the season left to play.
Everton were the better side in the first half but the home team applied more pressure as the game went on despite creating few clear chances.
"I feel sorry for them because maybe a point for them is fair," Mourinho told reporters. "But we were the team that was really trying to win."
The Portuguese again highlighted how Chelsea F.C. have struggled up front this season although he paid tribute to the team's progress in his first season back at the club.
"What I really feel is, to be where we are with 11 games to go, with some limitations we have in the team, that I think ... we are doing well," he said.
Mourinho added that he brought on hard-tackling Brazil midfielder Ramires at halftime, replacing his injured compatriot Oscar, because he was worried about Chelsea's lack of firepower.
"I felt I needed to control the game. If they had scored before us I think we are not a team in normal conditions able to score two goals and win the game," said the Portuguese.
Everton manager Roberto Martinez was frustrated at what he said was a "very soft" decision to give Chelsea the free kick that led to the only goal.
He added that Chelsea knew how to use "every trick in the book" to get free kicks in dangerous positions, helping them to make Stamford Bridge such a difficult venue for other sides.
"If you look at the record Chelsea have at home it must be more than playing well every week," Martinez said.