Chelsea made hard work of a 2-1 win over relegation-threatened Crystal Palace after Fernando Torres' opener was cancelled out by Marouane Chamakh, with Ramires netting what proved to be the winner in the first half.
Mourinho's men are now within two points of leaders Arsenal, who lost at Manchester City, and can assume the Premier League lead by winning at the Emirates Stadium on December 23.
Mourinho, who watched most of the second half of the match at the Etihad Stadium prior to kick-off at Stamford Bridge, said: "I'm not surprised because it's our nature. It's in this club's DNA over the years to try to fight for trophies.
"It's my way of work, too: it's the mentality we want the players to have. We all know this is a transitional period, we all know that we have just a few players from the winning side from the past. We all know we have lots of young talent to improve.
"I believe in another club with a different profile everybody would say 'OK, let's work and wait calmly, the results will come in the near future'.
"We are not like that. We want to build, but at the same time we want to fight for titles. And in this moment in the Premier League we are there, two points behind the leader."
Seamus Coleman's third Premier League goal of the season secured Everton's third win in four games and moved the Merseysiders to fourth.
Roberto Martinez's side held a 1-0 half-time lead through a Leon Osman goal on his 300th club appearance.
Dimitar Berbatov slotted his second penalty in as many league games to draw Fulham level at 1-1 in the second half. But defender Coleman's finish, a Gareth Barry header and a late Kevin Mirallas goal helped Everton to a 4-1 win.
Cardiff broke their three-and-a-half match goal duck when Peter Whittingham headed Craig Noone's cross home in the Welsh side's home clash with West Brom. After a goalless first half, Malky Mackay's side plundered the 1-0 lead just past the hour and it proved enough to guide them to their first league win in six matches.
Jay Rodriguez's second-half equaliser saw Southampton scramble a 1-1 draw at Newcastle. Yoan Gouffran's sixth goal of the season had handed Newcastle a 1-0 half-time lead.
Guy Demel had the ball in the back of the net for West Ham against Sunderland - but referee Andre Marriner ruled it out for a foul on Lee Cattermole and the match ended in a goalless draw.
Hull and Stoke drew 0-0 in the evening kick-off at the KC Stadium, where the visitors' Stephen Ireland had a goal disallowed for offside and Ryan Shawcross hit the crossbar.