The Hoops travelled to the tiny Samsungvollur stadium with a 2-0 advantage from last week’s first leg in Glasgow but found themselves under some unexpected pressure after only six minutes when Olafur Karl Finsen shot the home side into a shock lead.
However, midfielder Nir Bitton calmed the nerves when he levelled in the 32nd minute from a Stefan Johansen corner and further goals from defender Charlie Mulgrew, substitute Leigh Griffiths and Johansen made it 4-1 to see the Scottish champions through 6-1 on aggregate.
Deila’s side will play Qarabag in the third qualifier, with the first game at Celtic Park next week, and will sure to be tested to a greater degree against the Azerbaijan outfit, who came through their tie against Montenegro’s Rudar Pljevlja.
The Norwegian boss said: “We need to improve. They are a good team. I saw them play the first leg at home against the team from Montenegro and it is a big step up from what we have met here.
“I think we were a bit sloppy at the start of the game but we got the goal and we knew things were happening.
“In the second half there was only one team on the pitch and we won quite easily.
“We didn’t want to concede an early goal but it happens sometimes. We came back and 4-1 is a positive result and I am looking forward to the next round.”
Deila was critical of Stjarnan’s artificial pitch, which he claimed was not watered due to a broken pipe.
The Celtic boss said: “It is not a problem to play on an artificial pitch but when you don’t water the pitch it is totally different, everything is very sticky and everything goes much slower than usual.
“I always ask to water the pitch but it (water pipe) was broken this time – maybe it is ready again now.
“But that is how it is, we have to handle every circumstance and surface you play on and we made it, we are through to the next round.”