Higgins felt experienced midfielder Ryan Brennan showed his experience and 'manufactured' the penalty, which Dean Williams converted to earn the Drogs a share of the spoils.
The Candy Stripes boss was also adamant that the game should have been put to bed inside the opening ten minutes and his side should have been out of sight, but they failed to take their chances.
"I'm very disappointed, because the game should have been over after 10 minutes, as we should have been 3-0 up after 10/15 minutes and we should have had them dead and buried," he insisted.
"When you don't take your opportunities you get punished and we got nervy in the second half because we weren't further in front, they clawed their way back, got a penalty that they shouldn't have got and they put it away.
"I think we could have had two penalties in the one incident, there was a foul and then a handball, but we never got that one and they got theirs.
"I have seen it and you have got to know your players, do your homework, because it's not a penalty and we have been punished for it.
"They did get a foothold in the game but they didn't create a load of chances at all. I don't think they created any real chance of note, but Ryan Brennan has used his experience and street wise and manufactured the penalty for himself and we got punished for it.
"Having a 1-0 lead is nervy and as I said we should have been three or four up at half-time the game is dead and buried, so whenever you don't take your chances you can get nervous, especially the way things have gone recently and that's what happened.
"But when we're in those moments with a bit of difficulty we have to be better and show a bit more composure, but we move on."
The Limavady man was pleased by his team's overall performance, but was disappointed that they don't have that cutting edge in the final third.
"We weren't really creating chances in the previous couple of games against (Finn) Harps and Sligo (Rovers), but tonight we created seven or eight good chances and didn't put them away," he added.
"As I said when you don't take your chances at this level, it gives the opposition hope and they clawed their way back into the game, made it ugly, went direct and we struggled with it.
"I thought first half we were good and if you take your chances then you are asking me different questions, so as I said take your chances it's game over at half-time. In the second half we've got deeper because we didn't take our opportunities and sort of invited us on to us a wee bit and that's what happens in football, especially when you're not on a brilliant run and we've been punished again with a penalty, that should never have been."
To add to Higgins' problems is the mounting injury problems City are accumulating with Ronan Boyce and Eoin Toal now joining Ciaron Harkin and Michael Duffy on the injury list.
However young defender Caoimhin Porter, who slotted into right-back for Boyce, had a superb game before he too had to be substituted with an injury problem.
"Caoimhin did great, in the first half he put in three or four outstanding crosses, one after a minute or two when we should have scored, so he had a really good game, but he took a knock and we had to take him off," explained the 37-year-old manager.
"We were missing Ronan Boyce and Eoin Toal tonight, because they got injured in training over the last week or two, so we were down a few bodies again, but I still think if you analysis the game over the 90 minutes then we should have won the game comfortably.
"When you are without the likes of Eoin Toal, Boyce, (Ciaron) Harkin, (Michael) Duffy, who are key players from within your squad and players of that quality, then of course it's going to set you back.
"We need that winning feeling back. I know we didn't play brilliantly in the second half but we did create two/three really good chances and if you base it on chances and possession, then we should have won the game comfortably, but we didn't."