Neil Lennon's side played three Champions League qualifiers and six group stage games before exiting the competition, but only once did they fail to win following their return to domestic duties, drawing 2-2 at home to Inverness in the Scottish Premiership following a 2-0 first-leg qualifying defeat by Shakhter Karagandy in Kazakhstan.
The Parkhead club will have another shot at European football's elite club tournament next season after clinching the championship last Wednesday night with a 5-1 thumping of Partick Thistle at Firhill, although Saturday's home performance in the 1-1 draw against Ross County was less impressive.
Kris Commons' 28th goal of the season cancelled out a strike by Dutch striker Melvin de Leeuw for a share of the spoils from a game that failed to excite a bigger-than-normal Celtic crowd.
Brown, who admitted being culpable for County's goal by losing possession in the build-up, said: "This title win definitely ranks right up there with the others as it's been hard with so many Champions League games.
"Last season when we came back after Champions League games we struggled, dropped points and were beaten.
"This season after Champions League games we have been incredible and have won six games out of the six (following group-stage games).
"That shows just how much we are improving and next season we need to try to improve in the cups as well.
"My performance against County wasn't the best but I've enjoyed this season and I think that's the main thing. I enjoy playing for Celtic and I enjoy winning trophies. That's the reason why most of the lads are here."
A deserved, if unexpected point for Derek Adams' ninth-placed side keeps them three points ahead of St Mirren and one point ahead of Partick in their quest to avoid the relegation play-off spot.
The Staggies boss thought his side deserved to take more from the game but, with only one defeat in their last five games, he is happy with his side's form going into Friday night's Highland derby against Inverness in Dingwall.
"We finished fifth last season and this season we aim to finish top of the bottom six," Adams said.
"It's very tight at the bottom, there's six games to go and everyone's trying to get away from there. But we've been one of the form sides in the league since January.
"We've taken a point against Aberdeen and beaten St Johnstone, who are also top-six sides, and we've another game against a top-six side this week.
"It's difficult but the players enjoyed going to Celtic Park and I think you saw that from the performance.
"We've done well in the derby matches and we're really looking forward to it. It'll be a terrific occasion for both sides."