"We are not going to let up until the end of the season," the French midfielder said. "We are going to try to get points in every game and won't give up.
"Aston Villa have been fantastic and are in front of us, but we are really focused on our job and what is most important is what we are doing on the pitch.
"I think it was very important to get something from the game [at Everton]. We drew and took one point which I think is good for us because we were not so good.
"When you see the game, Everton were better than us and to take one point is very good here."
Everton took the lead through a well-taken header by Tim Cahill, and should have closed out the game in the dying minutes, their manager David Moyes ruing their failure to run the ball to the corner flag and whittle away time.
However, Robin van Persie was on hand with a first-class finish in the last minute of injury time. The Dutchman has now scored or created every one of his club's goals this year, a remarkable achievement.
"His first touch is unbelievable and that makes a big difference," Diaby said. "But we all try to play and give everything in each game and do our best to help the team."
Meanwhile, Arsenal have been dealt another injury blow with the news that experienced defender Mikael Silvestre has suffered an injury setback and will out for up to three weeks.
The former Manchester United player has been missing with a thigh injury since limping off against Plymouth in the FA Cup on Jan 3. He was expected to be close to a return but Wenger confirmed on Thursday night that he will be out "for two or three weeks more."
Arsenal crave enforcers not entertainers
When set against what Arsenal really need, buying Andrei Arshavin is akin to splashing out on a convertible in a monsoon.
The Russian will turn many heads, twist many defenders into submission, but such qualities are already provided by Robin van Persie, a beacon in a dark season, and Samir Nasri, an elegant influence when cutting in from the left.
Arshavin will doubtless be a success, as Arsene Wenger's purchases usually are, but Arsenal crave enforcers, not more entertainers. Central defence and central midfield must be bolstered if all Wenger's pass-crazed play-makers are to enjoy a proper stage for their talents.
By Henry Winter