The Hoops needed to avoid a 3-0 defeat or worse to make sure of third place in Group B.
And they did it in unfashionable style with defender Jozo Simunovic scoring an own goal just after the hour mark to hand three points to the Belgians.
Celtic finished their group campaign with just one win and five defeats.
But caption Scott Brown was nevertheless proud with the performance.
“We knew what we had to do and had to dig deep at some point and we managed to get through to the Europa League and that was our aim at the start,” he said.
“Yes, it was a little bit frustrating. The first half especially, we didn’t manage to keep the ball.
“They played their formation and kept the ball really well and were very, very patient and looked like they were the team that was going to score a goal in the first half.
“We still tried to play our normal game and play out from the back. They pressed us really high up the park and put us under a lot of pressure.”
Manager Brendan Rodgers said: “I think the context of the game affected our performance.
“Anderlecht having to chase the game, they were were far brighter.
“Midway through the first half, we had to change it tactically to stem the flow of the game, I was thankful to get in at 0-0 and we were far better in the second half.
“Overall, the best team won, but the bigger picture was to get through to the Europa League by finishing third and that would be a massive achievement.
“We were the fourth seeds coming into this and there is immense pride that we got the job done.
“But we have a lot of work to do at this level, but we can look forward to the Europa League in February.”
Full report to follow…