James Forrest came closest to opening the scoring in the first half when his right-footed shot rebounded off the crossbar.
Alexander was called into action once more before half time, as he kept out Nir Bitton's long-range effort.
Celtic's inaccuracy in front of goal cost them dearly. First, Scott Brown missed from long range before Commons and Griffiths both missed in quick succession.
With 14 minutes remaining, it was substitute Nadir Ciftci's turn to have a go but his shot went over the bar.
Bitton then rose highest from a corner but his header went wide of the right post.
Efe Ambrose was sent off in the 94th minute, but that made no difference to the scoreline as the match ended goalless.