Goals from left-back Emilio Izaguirre and striker Stefan Scepovic took the champions to within one point of leaders Aberdeen but with a game in hand before they fly out on Tuesday morning to Gran Canaria for their winter break.
The Hoops boss was pleased by the way his side bounced back from their goalless home draw against Ross County in their last outing, which came after a defeat at Dundee United.
The Norwegian said: "It was a good performance, particularly in the first half, and we scored two good goals.
"I think it was a very good answer from the players.
"I have said all the time that I believe in them and this performance shows what is in the group.
"It was the right response after the Ross County (match) when we had domination but didn't create enough chances.
"Today we had a better tempo and created the chances we needed to win the game.
"We are back on track again
We are going to continue winning games and if Aberdeen do the same then it is going to be a tight race all the way to the end.
"But we are going to do our job
We can speak at the beginning of April, with six or seven games left, about who is challenging for the title."
Kris Commons was given a rare start and hit the bar twice amid a deluge of shots on the Killie goal.
Deila conceded it was the type of performance which will keep the midfielder, out of contract in the summer, in his team.
He said: "Especially in the first half, Kris was very good - as was the team.
"He worked very hard
There were good reactions when we lost the ball and he created a lot of our chances.
"He did a lot of things well and that's what I wanted to see.
"Ninety minutes like that is what we want from Kris
If he does that, he is a very important player for us.
"We are talking together (about a new contract) and we will see if we can get agreement."
Killie manager Allan Johnston tried to take some comfort for his side's improved performance after the break.
He said: "Especially the first half, Celtic passed the ball really fast and they looked a lot sharper but in the second half I thought it was two different teams.
"In the second half we had more pressure on the ball but you can't afford to let good players have that time on the ball, especially in the first half.
"To be fair, it was better in the second half but we have to learn we can't start the way we started against Celtic."
Asked about reports that Killie were interested in bringing back Kris Boyd from Rangers, Johnston denied having made an enquiry but said: "You're obviously looking to see what players are available.
"I don't know if Boydy's available or not, obviously he's still contracted to Rangers but you're looking at all good players, not just Boydy.
"As it stands at this moment, we don't have any money to bring anyone in anyway."
Source : PA
Source: PA