"Cup football is all about getting into the next round and we have managed to do that," he said.
"My heart wasn't in my mouth, I think we were reasonably comfortable.
"I genuinely don't think they threatened our goal too much in the 90 minutes.
"The second goal would have had us sitting comfortably but ultimately we didn't need that.
"It wasn't as fluent as it has been over the past few months and I don't think it was ever going to be the case.
"It was going to be a difficult night but we managed to get into the next round."
Morton boss James Grady said his side were undone when they switched off for a moment in the first half, but he will be happy if his players produce similar performances in the First Division.
Grady said: "We started well and we were up for it from the start.
"We contained Celtic for long spells but I have to look at the goal.
"It was a cheap goal to give away in terms of it came from a throw-in when Fortune was getting marked on the wrong side.
"It is a basic error.
"He gets along the by-line and we were exposed.
"But I'm proud of the players, they gave us everything they had and I said to them that if they give us that performance then most weeks we will win games in the First Division.
"They have to treat teams like Dunfermline, Inverness and Airdrie the way we treated Celtic and then we will get ourselves in to a more realistic position."