The Hoops dominated possession in the first leg of their UEFA Champions League second qualifying round clash in Iceland, but struggled to break the deadlock.
Midfielder Callum McGregor, 21, was the man to finally end Reykjavik’s resistance in the 84th minute when he beat the previously impressive home goalkeeper Stefan Magnusson at his near post via a cruel deflection.
Deila said: "I am happy that we won the game but most happy with the performance.
"I love to win and I am here to win but I need performances. I want to win in a certain way as well.
"Today was a step forward in the way we want to play and that is what I am most happy about.
"We deserved it, we deserved more. I am getting energy out of this, I like what I saw in the second half."
McGregor was making his first competitive start for the Hoops after impressing in pre-season and Deila was impressed, adding: "I think he did well in his debut, in an important match like this.
"He has big talent but I want him to be more direct, go forward more and link up more with the full-back. But that will come and I am very happy for him that he scored a goal."
McGregor, who had a successful loan spell at Notts County last season, was thrilled to open his account for Celtic.
The Scotland U21 midfielder said: "To score in a Champions League game for Celtic was a dream come true. I have been there since I was nine years old.
"It was a big night for the club to strive to get Champions League football again and that might be the goal that takes us through to the next round, so I am absolutely delighted.
"To get the win was excellent for the team and, on a personal note, to score the winning goal was unbelievable. I am still pinching myself to see if it's real.
"I spent last season with Notts County in League One and I feel I have come back a better player.
"When you come back here you don't want to leave. Being at Celtic means the world to me so, if I can be here for a long time, I will be delighted."
KR Reykjavik boss Runar Kristinsson said: "It was a bit disappointing but I think it was a fair result.
"It is still alive, 1-0 is nothing in football.
"It is going to be very difficult but, if we can defend well and go to Scotland with a good attitude, we believe we can do something there, at least give them another game, because I think we did that today."
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