The Parkhead men could end up with an SPL and William Hill Scottish Cup double - they play Hearts in the semi-final at Hampden next week - but their Europa League campaign was less successful, bringing only one win in eight games.
The former Celtic skipper, though, believes his side have improved in the intervening months and, with a bit of bolstering, will be looking for them to get through their two Champions League qualifiers next season.
"We want to improve the club's status in Europe if we can but again, that's a hard thing to do," said Lennon.
"But I think it is important, looking at the Champions League qualifiers, it will be important now to get into the group stages.
"We will have to look at the close-season programme and our pre-season and try to get a recipe to get that right for the qualifiers because it would enhance the season no end and give these players a huge shot in the arm in terms of their own development.
"There's no doubt we have to trim the squad a little bit, we will look to do that and maybe enhance the squad with two or three players of undoubted quality.
"But that's for the future, for the here and now I am delighted for the supporters, they have been behind this team since I took over."
A Charlie Mulgrew double and goals from stopper Glenn Loovens and striker Gary Hooper had the title party in full swing well before the break.
In front of a huge travelling support which took up three stands, and brought Kilmarnock a reported £150,000 bonus in gate receipts, late goals by Joe Ledley and Hooper put another coat of gloss on an emphatic win.
It was an afternoon of stark contrast to Celtic's visit to Rugby Park on October 15 last year.
Lennon had considered his future going in to the dressing room at the interval 3-0 down before his side rallied in the second half to grab a draw which kept them on the coat tails of then leaders, Rangers.
The Northern Irishman said: "Football is unpredictable and nothing surprises me.
"I always believed in the team and always felt we would find our consistency but worried that it would be too late.
"But we found it and put a fantastic run together of 17 or 18 wins and that is special in any level of football.
"And to play the way they did yesterday [Sunday], confirmed that they are the champions without any question of doubt."
For the second successive season Kenny Shiels suffered the ignominy of an Old Firm club celebrating a title win at Rugby Park following a convincing win.
Rangers thrashed Killie 5-1 last season to retain their title and while Saturday's scoreline was even more depressing for the home fans, Shiels claims his side did themselves no favours with their lax defending.
"You are given a job to pick up players at set-pieces," he said. "The first two goals conceded were from set-pieces, one direct from a corner, one from a second-phase corner and that's just not good enough.
"They are worthy champions but we have players who need to do better and we are working all the time to do that."