"I'm disappointed. That's my over-riding feeling at this moment in time.
"Things may change tomorrow when I have a chance to analyse the match and have a look at the performance. But we were winning the match with minutes to go so I feel disappointed.
"The players are frustrated, some are angry and others are just disappointed."
Levein admits his players are maybe still lacking a bit of confidence in themselves when they travel to venues like Ibrox.
He added: "I can't give the players belief in themselves just by telling them they are good players, they have to actually experience it.
"They are all gradually growing in confidence and they are all absolutely gutted that they didn't win this match.
"I can speak to them tomorrow and we can look at the positives from the game and look at things we can do better."