The Scottish champions eventually advanced to the third qualifying round thanks to Bitton’s equaliser and second-half goals from Charlie Mulgrew, Leigh Griffiths and Stefan Johansen.
However, Ronny Deila’s side, who took a 2-0 first-leg advantage to the tiny Samsungvollur Stadium, were given a scare after just six minutes when Olafur Karl Finsen put the home side in front.
Israel international Bitton admitted he was concerned when Stjarnan opened the scoring before his side ran out 6-1 winners on aggregate.
“I think everybody was worried,” he said. “We didn’t want to start the game like that and concede a goal after six minutes, it wasn’t the game plan but sometimes you need to deal with this kind of thing.
“The most important thing is that we go through to the next round and we just want to continue.
“I am really happy, not because of my goal but because we won the game. My goal was a bonus.”
The Hoops will play Azerbaijan side Qarabag in the third qualifier, with the first game at Celtic Park next week.