However, three minutes later the Hoops left-back, on loan from Bayern Munich, mistimed his jump and handled the ball inside the penalty area, giving Steve MacLean the chance to reduce the deficit.
The Dons striker later dramatically levelled with two minutes left to dent Celtic's title hopes.
Rangers will have the chance to go 10 points clear again at the top of the Scottish Premier League when they play against Hibernian at Ibrox on Sunday.
Mowbray looked downbeat to say the least after the 4-4 draw, knowing his team passed up the chance to put the pressure on the Govan men.
"It is disappointing to lose the lead three times," he said.
"The game is never over but it should have been.
"At 4-2 their 'keeper made two great saves and it looked like the flow was going our way but we gave them a lifeline by conceding a penalty kick which was unexplainable.
"Can you explain it?
"The performance was not very good and the result was not very good but we got one point and we will wait and see."
Mowbray added: "I won't make excuses but we had a few defensive problems with injuries to key players.
"I'd like to think if we had more options we wouldn't have conceded the goals we did, but we did and we move on.
"We are functioning in one part of the pitch but not another, let's hope Hooiveld, Loovens and Hinkel are back pretty quickly.
"Let's judge us when we get the injured players back."
An exhilarating first half ended level after goals from Diomansy Kamara and Marc-Antoine Fortune had been cancelled out by Michael Paton and Darren Mackie.
The visitors went two clear with goals from Robbie Keane and McGeady, but their late collapse - and the sending-off of defender Darren O'Dea for picking up two yellow cards - will have been savoured by Rangers.
Aberdeen boss Mark McGhee had been involved in some controversy before the game.
However, contrary to speculation, he did not field a weakened team ahead of Tuesday's Scottish Cup fifth-round replay against Raith Rovers which extinguished immediately any conspiracy theories suggesting the former Celtic striker was helping his old club.
McGhee had been raging at such suggestions and consequently cancelled his pre-match press conference on Friday.
After taking the point from Celtic, he hit out at sections of the media.
"It was scandalous the way it was spun," the former Celtic and Aberdeen striker said.
"The people who wrote that disappointed me because as far as I'm concerned they questioned my professional integrity.
"It is insulting to me and I feel I was betrayed.
"I was talking to Walter Smith at Hampden on Thursday and the most important person to ask if he had any doubts as to my commitment to beating Celtic is Walter.
"I have tried very hard to cultivate relationships with the press, appreciate what they have to do and help them as much as I can.
"I will say it again, I was brought up a Celtic supporter, like all of us we have a club and that doesn't change,
"But I wanted to walk down Byres Road (in Glasgow) and look Rangers fans in the eye with them knowing that I am trying to take points off Celtic as well as Rangers.
"I will leave Aberdeen fans to judge for themselves as to our commitment and determination to take something out of the game."
McGhee believed his side could still recover even when they went two down in the second half.
He said: "We could have done better defensively but even at 4-2 I still thought we could get back in the game.
"I felt if we could get a goal back quick enough then we could something from the game so I wasn't surprised when the fourth goal went in."