With rivals Dundee United securing a late 2-1 win at Ross County, the Steelmen were leapfrogged by the Arabs as United finished the season in fourth place on 48 points, two more than ’Well.
So the Fir Parkers will enter next season’s Europa Conference League in the second qualifying round, a round before United.
Saturday’s defeat saw Celtic goals scored by Kyogo Furuhashi (2), David Turnbull, Jota and Giorgos Giakoumakis (2).
"We had to change the team 55 minutes before coming here because of illness,” said ’Well boss Graham Alexander said. “But we came up against a fantastic team on a massive high.
"We need to look at the season as a whole as we have done some fantastic things getting into Europe.
"We can't just focus on European football. We need to strengthen and remember the league programme as well. You will see the other big clubs at this level improving a lot.
"They will spend a lot of money so we need to work exceptionally hard to improve what we have if we want to stay as competitive as we have been this season.
"We have quite a lot of contracted players, lads for the future, lads for now. But we have to improve.
"There are certain things in our results that we have to get better at. We have done a lot of good things this season but we have always been aware of where we need to be better.
"So if we can improve certain aspects of our squad and our team then we have to do that. I feel we have a nucleus of a good squad."
Motherwell have conceded 62 goals this season despite their fifth place finish. Only bottom club Dundee with 63 let in more.
"Our defensive record is not good enough,” Alexander added. “Plain and simple.
"We have scored a lot of goals this season but we have to look at the structure, how we set up, a lot of things, but the goals against, if you look over the course of the season, have hurt us a little but so we have to look at that."