The Parkhead men led from the first leg of the third round qualifier through a Dedryck Boyata goal and more than held their own in the return game at the Tofiq Bahramov Stadium, despite surrendering possession for large spells and seeing out five nervy minutes of added time.
Afterwards the Norwegian boss, who passed up two chances to get into European football's elite club competition last season after taking over from Neil Lennon, said: "I'm very, very happy
"It was an exciting game, right to the end there was so much nerves
I am proud of the team spirit that we had tonight.
"The midfield won balls all over the pitch and the defence was tight behind them.
"Defensively we were very, very good, and offensively we should have punished them more when we won the ball in so many good situations.
"But it was hot out there and the players got tired against a good team when they kept the ball
I'm just very happy and proud of the boys.
"Last season we talked about losing too many goals
In the league we were very good in defence and now we have also done it in Europe and that is a very good improvement."
Deila was quick to praise Qarabag, claiming they are as good anyone left in the qualifying section of the tournament.
He said: "I admire Qarabag
"I think they are a very, very good football team, the way they play I hope to see Celtic play like that in the future with no fear on the ball - attacking football.
"That's what we want to do in Europe so a lot of credit to them
But you saw that we were a team, staying together with good communication and a lot of discipline.
"They had a lot of legs, a lot of running all over the pitch for 90 minutes, winning balls all over, and then we can improve the play as well."
Source : PA
Source: PA