Freddy Eastwood and Carl Baker scored within 20 minutes as the Sky Blues dominated most of the play, but Neil Danns' 81st-minute strike for the Eagles set up a tense final act in which the midfielder shot tamely at Keiren Westwood from the penalty spot.
Freeman, who does not expect to be in charge of Palace's next match, said: "I think we should have ended up winning the game if we look at the chances and the possession we had, especially in the second half.
"We missed a penalty and one or two close shaves in and around the six-yard box so overall I thought we could have won it, but if you switch off in the first 20 minutes and don't defend properly you are going to get punished.
"I probably won't be in charge for the next match. I think we should expect a new manager sooner rather than later and the only reason I say that is because we are in the transfer window and you can see that we are short in one or two positions and I think it is best that we appoint a manager so that he can get into the transfer market."