Steven Gerrard's Rangers was punished for spurning scoring chances when Celtic defender Christopher Jullien knocked in a free kick from Ryan Christie in the 59th minute.
Admitting that he was reluctant to comment on matching McNeill's record in the build-up to the match, Lennon was full of praise for the manner in which Celtic, inspired by goalkeeper Fraser Forster who saved a penalty from Alfredo Morelos, secured a 10th consecutive domestic trophy triumph.
Forster was quite simply outstanding against Rangers, coming to Celtic's rescue on a number of occasions.
He told the BBC after the match, "As long as you win, that's all that matters".
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"They were fantastic in front of me and when we went down to 10 men we defended really well". It's easy to give it up, to think "Oh, it's not our day today and that's the end of it" but they just won't. I've had some special days and I am just buzzing I did my bit for the team.
"I didn't want to talk about it (equalling McNeill) before the game but it means the world to me", said Lennon. I didn't really think about the penalty to be honest.
"Forster has played 19 games since going back up there and when you look at him, two seasons ago he wasn't a fraction of the man that Southampton paid £10million".
Substitute Michael Johnston inexplicably fired wide after being played clean through, while there was still time for one final Morelos miss - the forward dragging narrowly wide deep into stoppage time, as Celtic held on for yet another win in a major final. We're so thankful to have him here. We needed him today.
We won, we won ten trophies in a row! It owed me one.