"We had 26 corners, hit the post and had one cleared off the line. I've got to give credit to Morton who defended heroically at times.
"Did we do enough to win the game? Yes, but we didn't take our chances so, congratulations to Morton."
Moore agreed with the defensive performance of his side.
"We defended brilliantly," he said. "We rode our luck in extra time but the fact they stuck a centre-half [Virgil van Dijk] up front was testament to how well the team played.
"We knew we'd need to batten down the hatches and throw our bodies in front of things. Our goalkeeper didn't have any outstanding saves to make."
Although reluctant to pick a man of the match, Moore highlighted the contribution made by Slovakian defender Tomas Peciar and French midfielder Fouad Bachirou.
"Some of the headers Peciar won, in his first full game for us, towards the end were magnificent," he said.
"Freddy [Bachirou] can step up. He has been outstanding in our league games. No disrespect, but playing in a better team in a higher league would bring him on leaps and bounds."
Moore praised the Cappielow chairman Douglas Rae for his patience while the team has struggled this season and said he hoped the League Cup result would "be the catalyst for picking up points" in the league.
"I hope we can keep these standards up and push on in the league because that is our bread and butter," he added.
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