Ballinamallard United boss Gavin Dykes was happy with the draw, but reckons his boys threw away the chance of taking all three points.
The basement sides in the Danske Premiership fought out a 2-2 draw at the Loughshore Hotel Arena.
Joshua McIlwaine struck an 83rd-minute equaliser to give bottom side Ballinamallard a point.
James McKenna blasted the Mallards ahead before a half-time altercation led to both managers being sent off.
Carrick hit back on the restart and moved in front with headed finishes from Michael Smith and Denver Gage.
Dykes said: “In all honesty, I thought we were the better side.
“I thought we were the only team that tried to play a bit of football.
“There’s no doubt we deserved to be in front at half-time.
“Unfortunately, we never got going after they break and they hit us with two quick goals.
“But again the team showed their character to come back an equalise.
“We came looking for three points. We are disappointed we didn’t get them, but at least we left with something to show for our efforts.
“There were a lot of positives to take from the game.
“I have a lot of good players in that dressing room and I know the second half of the season will be a lot better for us.
“I hope to add a few new players to the squad in January.
“Hopefully, we can start moving in the fright direction.
“At half time, I went to get my captain off the pitch because he was getting some abuse.
“It was what the fourth official told me to do.
“Davy (McAlinden) then came charging at me as I was trying to hold my captain back.
“I did absolutely nothing. It was a ridiculous decision.
“And, I have no problem with Davy. There was a lot of passion because it was a big game for both clubs.”