Leigh Griffiths had given his side a 35th-minute lead from the penalty spot before teammate Dedryck Boyata saw red seven minutes later for a lunge on Carlton Morris.
Gary Mackay-Steven and Griffiths both spurned chances to double Celtic's advantage before the Scotland striker saw his second penalty of the match saved by Hamilton stopper Michael McGovern.
Hamilton then grabbed a superb 73rd-minute equaliser through substitute Eamonn Brophy as they gained some redemption for their 8-1 humbling by the Hoops back in January.
It ends a run of three successive wins for Celtic and the Parkhead club's manager was angry at his side's lack of composure in front of goal.
"It's disappointing that we went down to 10 men and we didn't win this game," Deila said.
"We started well but in the second half things were more open. You have to take your chances especially when you are down to 10 men.
"We had three very big chances and didn't score and they got theirs from a set play and that was disappointing.
"I think we defended in the second half better than we have with 10 men before and they didn't have a lot of chances and we had a lot of control. But we needed to want the ball more and create more chances and maybe have been braver on the ball.
"Leigh missed the penalty and he was two times alone with the goalkeeper as well so that's hard to swallow. We had three very big chances and should have won the game."
Boyata's red card for bringing down Morris had a big influence on the game and television replays appeared to suggest the Belgian defender got something on the ball first.
However, Delia said he had no argument with referee Craig Thompson's decision.
"The sending off is an okay decision. He doesn't take the ball and we have to start learning that you have to stay on your feet and run with the player in those situations," the Norwegian manager said.
"I've seen it one more time and he doesn't take the ball so it's a red card."
The point means Celtic open a seven-point gap at the top of the table over Aberdeen, who could cut the deficit if they can defeat St Johnstone on Saturday.
"There are 11 matches left and a lot to play for. Nothing is finished here and I say that all the time," said Deila, whose side host Dundee on Wednesday.
"But we are going to fight to the last game and already on Wednesday we have a game where we want three points."
Hamilton manager Martin Canning was proud of the progress his side had made since their 8-1 humiliation at Celtic Park.
"The team worked ever so hard and deserved something from the game," Canning said.
"Michael McGovern kept us in it with the penalty save and then we got our goal but with a bit of luck we might have got all three points.
"I'm proud of the boys as it's such a big effort to take something off Celtic, albeit with ten men, but you have to put in the work."