The big (Captain Obvious) difference between teams like Celtic and ourselves is the quality of the players. And by that I mean, when we made 4 mistakes, they were good enough to score 4 goals. When they make mistakes, we don't capitalise as often.
We can dominate possession, high press, make chances etc. but the deciding factor will always be making those chances count and punishing mistakes. That edge is what Celtic's money can buy to dominate in the Premiership, but is much less of an advantage in Europe.
As an aside, as much as I dislike the OF, I still think it's ridiculous that a team that wins its domestic league is asked to go through qualifying rounds while teams that finish 2nd or 3rd in other leagues are not. The Champions League already provides enough advantages for the big teams without handing them automatic qualifying on the basis of "they have plenty of money already".