"I'm stunned," Mowbray told ESPN. "I really thought the game was finished at 4-2 but we inexplicably gave them a lifeline, they grabbed it late on and it's a frustrating day for us."
The manager said he was particularly disappointed at how his side had coped with high balls into the box against a side who were not well known for posing an aerial threat.
"They pushed very hard for the equaliser and ultimately got it but we talked before the game about our defensive problems and we didn't stand up to what came our way today," he said.
"We scored some great goals but lost poor goals to set-plays and sometimes you need someone to go and head the ball...Aberdeen don't have huge height in their side."
Mowbray took Robbie Keane off after the striker has scored his first SPL goal for Celtic and explained that the substitution for Georgios Samaras was intended to help the inexperienced defence cope with pressure from Aberdeen.
"[Keane’s] not a giant, he doesn't stand and head corners away for us,” Mowbray explained.
"Georgios Samaras does - he's 6ft 3in - and that was part of the thinking. I don't think it had any relevance in the game."
The manager remained hopeful that Rangers would drop points in the title race. He said that if Hibs could record a win at Ibrox then his side would still have gained ground on the SPL leaders.
"It's a point for us. I don't know what the results will be later, or tomorrow. It might be a point gained, we'll wait and see."