Deila said: “Overall, it is my responsibility. If that is not good enough, then it is not good enough.
“It was a very hard game, but we now have to fight for the league. We have a very good chance, but there are still five games left, so we look at it after that. In football, you never know.”
The Hoops gaffer admitted his side were “too passive” in their pressing of their opponents in the opening 45 minutes and goalkeeper Craig Gordon agreed their start to the game ultimately cost them.
He said: “We should have performed better in the first-half. If we had done that, we probably would have gone on to win the game.
“I didn’t think Rangers (sic) carried a great threat after half-time. I thought we were the better team once they had scored their second goal and we had chances to go on and win it.”
Gordon claimed referee Craig Thomson wrongly awarded the Ibrox side a shy in the build-up to Barrie McKay’s extra-time strike which put them 2-1 up.
He said: “The throw-in has gone the wrong way. Three players are in front of the referee and he has got involved in something else.
“That said, we should have defended it better, but it was a one-hit wonder. He could probably have hit it another 100 times and not hit it as well.”
“It is a sore result to take, especially here in a derby match and emotions are raw. The fans are going to be unhappy about it.
“It is up to us to fight back. It is very difficult after a result like that, but we have to do that now and go and win the league.