Stuttering Madrid, who have already lost more competitive matches this season than they did in the whole of the last campaign, were held to a 2-2 draw by second-bottom Espanyol at the Bernabeu after conceding an 88th-minute equaliser to Juan Albin.
To compound Madrid's misery, arch rivals Barcelona beat Atletico Madrid 4-1 in the top-of-the-table encounter at the Nou Camp in the evening's late kick-off to stretch their lead over the defending champions to 13 points.
Although he insists his side will not give up the fight, Mourinho believes that gap could now be too large for his side to make up.
Speaking before Barcelona's win over Atletico, Mourinho told reporters: "It's practically impossible. It's 10 points which could become 13. 13 points in December are a lot. We had eight last year and despite drawing two matches we maintained that distance."
Although the league title may be slipping from his side's grasp, Madrid have progressed through to the last 16 of the Champions League and would secure a quarter-final berth in the Copa del Rey if they can overturn Wednesday's 2-1 first leg loss to Celta Vigo in the return meeting at the Bernabeu.
Mourinho said: "We will try to finish the season as well as possible.
"If we improve in La Liga, it would help us to improve in the Copa del Rey and in the Champions League, where we have chances to be stronger.
"We can't worry about finishing first, second or third. We have to be stronger."
Sunday's result left Madrid with 10 wins, three draws and three defeats from their opening 16 league games. Last season they finished with 32 wins, four draws and just two defeats while earning a record-breaking 100 point haul.
Mourinho said: "It seems crucial that we try to improve. I've never seen a situation where there's been so many points lost and that a team of mine was so far from its objective. It's a new situation for me.
"The league is almost impossible, but we need to continue, Real Madrid demand the maximum dignity. In my coaching career I've always, or almost always, achieved my objectives and this is new for me."