Celtic cruised through to the third qualifying round with a 6-1 win over Icelandic side Stjarnan but Deila believes the Azerbaijani champions will be a major obstacle.
Qarabag were only denied a Europa League win over Inter Milan last season by a poor offside decision which cost them a place in the knockout stages.
Celtic also drew with Inter at Parkhead before going out 4-3 on aggregate and Deila has told his players they need a similar performance at Celtic Park on Wednesday.
And the Norwegian appealed to supporters to fill the stadium to give his side every help possible.
Deila, whose side host French outfit Rennes in a friendly on Saturday, said: “It’s a big, big step up. We are talking about a very good football team who have done very well in the Europa League.
“They beat Dnipro, who were in the final, and (drew with) Inter Milan as well.
“So we have to be up at the Inter Milan level that we were to beat them, which is going to be a fantastic challenge for us.
“We have to create the performance we did against Inter Milan, and then we also need the fans in Celtic Park on Wednesday.
“That’s so unbelievably important, because to play at Celtic Park against 60,000 fans is the worst thing you can do as an opponent.
“We have to use everything we have to make a good result in the first leg. Hopefully everyone understands that the fans are so important to get the intensity into the game that we need.
“It strikes fear in everybody. We have the best fans in the world and we have to show that on Wednesday.”