Ange Postecoglou commended his players for their response following two blunders that put them under pressure against AZ Alkmaar.
With just over two minutes on the clock in Holland, Kyogo Furuhashi put Celtic 3-0 ahead on aggregate, but Joe Hart was punished three minutes later when the hosts equalized.
AZ took the lead in the 26th minute when Carl Starfelt put the ball into his own net under no pressure, but Celtic came out on top 3-2 on aggregate to qualify for the Europa League group stage.
“It was hugely important we got through,” Postecoglou said.
“It means we are going to be playing in one of the elite competitions against good-quality opponents and ensuring there are more special European nights.
“We made two pretty terrible errors but that’s what happens when you’re dealing with human beings, they’re going to make mistakes. What was more important for us is how we reacted.
“We lost our way a little bit in the first half and they got some momentum, because we started the game well. Obviously giving them two goals set us back but the second half we dug in when we had to.
“Joe, who was disappointed with the first-half mistake, made a couple of outstanding saves and Carl defended really strongly in the second half.
“I thought we were a little bit more composed than we were in the first half.
“It was a different type of performance but it’s great that we showed that resilience.”
“It’s too early to tell about Greg,” said Postecoglou, whose team face Rangers at Ibrox on Sunday.
“I thought Monty was outstanding, coming on, a young player, knowing we would have to defend a fair bit.
“Kyogo got a bit of a knock and the rest of them put in a shift so it’s going to be all about recovery for the next 24-48 hours and then we will see how everybody is.”