The Blues restored their six-point lead over Manchester City with a 3-2 win over spirited Hull on Sunday and retain a game in hand against rock-bottom Leicester.
That makes them heavy favourites to lift the trophy and Mourinho was happy to accept the role of front-runners after Loic Remy grabbed a 77th-minute winner at the KC Stadium.
"I'm not pretty sure, I'm pretty confident
I believe in my players, I believe that we can do it but I know it's difficult," he said.
"I keep thinking the same, the title race should be over
In normal conditions, Chelsea should have eight, 10, 12 points more than we have; title race over.
"But football is unpredictable and the reality is we have a six-point lead, one game in hand, which is our best situation for the whole season."
Costa's short-term involvement is an open question, though.
The Spain striker claimed his 20th goal of the season with a wonderful curling effort to put Chelsea 2-0 up inside nine minutes following Eden Hazard's opener, but Costa hobbled off with a hamstring injury.
His exit allowed for Remy's match-winning arrival, but whether he emerges from the imminent international break in match condition is uncertain.
"When a striker is playing, the team needs a goal to win the game and with 15 minutes to go the striker, a guy with a lot of experience of hamstring injuries, says 'it is over for me', then it is over for him," said Mourinho.
"He has this problem
He tried to play the Champions League final for Atletico (Madrid, last season) and was injured again and again and again
He has this fragility.
"We know his hamstring is not a strong one
He works hard through the week to compensate the weakness he has there but the injury can come.
"If he is injured then we have Remy, we have Drogba
we never cry about injured players."
Costa can at least expect to miss Spain's forthcoming games against Ukraine and Holland, but despite the added rehabilitation time, Mourinho would rather be pressing on with the domestic calendar.
"For Diego (the break) is good, because imagine we play three matches in one week, that's three matches he doesn't play," the Portuguese added.
"But in this moment we have nine matches to play and I would like to play every week, so it's not good for us."
Chelsea goalkeeper Thibaut Courtois gifted Abel Hernandez an equaliser just a minute after Ahmed Elmohamady made it 2-1, side-footing a back pass straight to the City striker.
But Tigers boss Steve Bruce believes the Belgian's brilliance later in the piece was crucial to the outcome.
Courtois produced a sensational triple save from Elmohamady, Jake Livermore and Gaston Ramirez in the 64th minute to keep the scores level.
"The big turning point in the game was where Courtois pulls off three saves which change the course of the game," said Bruce, who was nevertheless delighted with his side's endeavour.
"That's as good as we've played for a long, long time, against the best team in England.
"We're obviously disappointed to lose the game because I don't think we deserved that.
"We gave Chelsea a hell of a run for their money and on another day it could have gone our way.
"I'm sure we've got enough and I'm convinced if we play like that, we're good enough to stay in this division."
Source : PA
Source: PA