Chelsea play Southampton on Wednesday after finishing 2013 in third place, two points behind leaders Arsenal and one behind City.
Merely being in contention is an improvement on recent seasons for Chelsea, who have won one Premier League title since Mourinho's first spell as boss ended in September 2007, when Carlo Ancelotti led the Blues to the double in 2009/10.
Mourinho, who guided Chelsea to successive titles in 2004/05 and 2005/06, said: "Last year in this moment we were 12 or 11 points behind the leader, so game over.
"In this moment we are two points behind, so game on. Let's keep going."
Mourinho is a fine exponent of the mind games which Sir Alex Ferguson enjoyed playing as Manchester United boss and again talked up 2012 champions City after beating Liverpool.
He added: "Do you think I'm putting pressure (on City)? You think I'm capable of it?
"See the squad, see the players, the number of goals, the strikers.
"(Edin) Dzeko is the third striker of Man City. Dzeko.
"(Stevan) Jovetic, the fourth."
The mention of Dzeko and then Jovetic was followed by a resigned exclamation at City's resources before Mourinho insisted Manuel Pellegrini's side are fully aware of their talent and potential.
Mourinho added: "I think they know how good they are and I think they know they are the favourites. I don't think they feel any pressure."
Chelsea are hardly the poor relations in the Premier League, but while Mourinho looks enviously at other striking resources, he insists the Blues have no plans to bolster the forward ranks during the winter transfer window.
Chelsea's strikers have six Premier League goals between them this season - Samuel Eto'o (three), Fernando Torres (two) and Demba Ba (one) - compared to 19 for Liverpool's Luis Suarez and 13 for Sergio Aguero of Manchester City.
"I'm happy with them," Mourinho said.
"I keep saying that they are not this profile of player that scores every weekend and scores 20, 25, 30 goals in a season.
"But they are giving everything they have and I am happy with them. "No new strikers in January, because we trust these guys and we go with them."
If Chelsea had a Suarez or Aguero, some commentators argue they would be clear at the top of the standings.
But, for now, Mourinho says Chelsea must target a place in the top four and Champions League qualification and then see where it takes them.
He added: "This season the top four will be a big achievement for everyone.
"The difference between the top four and being champion, it looks like it's not a big difference, so I think the first objective for everyone is to attack the top four.
"And if we can protect the top four, let's see what we can do and let's see if Man City kills everybody or if they keep being close to all of us."
Mourinho maintains there are still six sides vying for the title - and Chelsea are yet to be beaten by any of them.
At Stamford Bridge, where Chelsea have won nine and drawn one of their 10 games - a home record only bettered by Manchester City's at the Etihad Stadium - Mourinho's men have beaten City and Liverpool.
Draws have been picked up at Manchester United, Tottenham and Arsenal.
United are sixth, six points behind Arsenal, after a recent resurgence, while Tottenham are seventh, behind the defending champions on goal difference.
"I think the six are (still) there," Mourinho added.
"Of course, Everton and Newcastle are close to the top four, but I think Tottenham and Man United are ready to attack the top four.
"When they (United) were 10, 15 points behind and losing at home, I was saying Man United are Man United. Tradition plays a big part, so Man United is there ready to jump into the top four and to give a fight to everyone."
Southampton were in the top four earlier this season in a surprise rise under Mauricio Pochettino.
Chelsea suffered a fright against Saints on December 1, conceding a goal after 13 seconds, before winning 3-1 and Mourinho knows his side have to be on their guard at St Mary's Stadium in a match made more difficult due to injuries to Frank Lampard and Branislav Ivanovic.
"Another good team," Mourinho said.
"At Southampton, especially, I think they feel very comfortable. So (a) very difficult match."