Pars force Rangers replay
In the end, following an entertaining 1-1 draw, the two sides will have to settle their quarter-final tie at Ibrox in a replay on Wednesday April 9.
Substitute Shota Arveladze was guilty of a glaring miss from close range and goalscorer Claudio Caniggia missed two good later openings.
McLeish said: “In the second half we had the chances. From the dugout it was difficult to see how close in they were but they did look pretty gilt-edged and we have really got to be burying chances in those situations.”
Rangers also finished with 10 men after captain Barry Ferguson was dismissed near the end for kicking Dunfermline substitute Noel Hunt. The pair had already clashed after the Irishman reacted angrily to a foul by Craig Moore.
Ferguson was shown a straight red so will miss the next game, a league clash with Partick, although he could also miss the replay if the penalty points he will receive take him over the threshold when added to his existing total.