A mostly uneventful stalemate in 90 minutes ensured another half-hour's play and five minutes into the extra period, the Ton midfielder Dougie Imrie scored from the spot after referee Bobby Madden adjudged Celtic defender Efe Ambrose to have handled when challenging Greenock substitute Archie Campbell.
The Hoops bombarded the Morton goal but despite 27 corners and numerous efforts on goal, they could not draw level leaving the delighted Championship side to take the plaudits from the travelling support at the final whistle
The Celtic boss said: "I have got to be philosophical about it. It wasn't for the attitude or want of trying in the game.
"It just wasn't our night for whatever reason.
"The only disappointment for me is we had 26 corners and we didn't convert one of them with the height we had in the team.
"We have to take our chances.
"We ended up putting Virgil van Dijk up to give us something different and certainly we created a lot more."