The second-placed Blues head for Stoke on Saturday having secured just their third league win on the road in seven attempts this season in thrilling style at struggling Sunderland.
With the Gunners beating Hull 2-0 at the Emirates Stadium, Mourinho's men needed to see off the Black Cats to remain within four points, and that will be the challenge once again at the weekend.
The Portuguese said: "We have two matches away from home consecutively while Arsenal have two matches at home consecutively, and that normally gives them more chance to win the six points.
"It was important for us to try not to let them open the gap. But this league is a league where in the top part and also in the low part of the table, any result can happen.
"Every point you get, you get with both hands because every point is difficult."
Jozy Altidore's first league goal for the club got Sunderland off to the perfect start at the Stadium of Light, but his 14th-minute strike was cancelled out by Frank Lampard when he headed home Eden Hazard's cross three minutes later.
The hugely impressive Hazard blasted the visitors ahead with a fine strike eight minutes before the break and after John O'Shea had levelled, repeated the dose with 62 minutes gone.
Fellow defender Phil Bardsley then got in on the act at both ends, turning substitute Demba's cross into his own net seconds before making it 4-3 at the other end as time ran down.
Chelsea's evening might have been far more straightforward had striker Fernando Torres taken any of the three gilt-edged chances which came his way, but Mourinho was happy with the Spain international's contribution.
He said: "He worked fantastically for the team. He did fantastic work for them. He played against two very experienced defenders in Wes Brown and John O'Shea and gave them a fight.
"He opened spaces for the other guys. He missed chances, but he was there."
Opposite number Gus Poyet was left to reflect on a spirited performance, but ultimately a defeat which left the Black Cats still at the bottom of the table and five points adrift of safety as they prepare to welcome Tottenham to Wearside on Saturday evening.
Poyet said: "It's a mix of emotions. You are devastated because you lost, you conceded four goals at home, you scored three against Chelsea and you didn't take even one point.
"That's football at this level. You cannot make any little mistakes against top teams.
"But if I remember my first one, how we lost 4-0 against Swansea, and I compare it with this one, what a change. It's a totally different attitude, two very different ways of playing football and commitment.
"I think we are [heading] in the right direction. Now I need to confirm that with a win. We can't keep talking and talking and talking - it's about winning football games."