The Reds went ahead after 17 minutes when Stephen Mallon broke following a Carrick free-kick before sliding it into the path of Rory Hale for the midfielder’s fifth Premiership goal of the season.
King felt his side should have had a penalty when Ben Tilney’s cross seemingly struck Jonny Addis’ arm on the stroke of half-time, but referee Evan Boyce waved away their appeals.
Ronan Hale then continued his superb return to action by scoring in a third consecutive game with a glorious lob after latching onto a long ball over the top before Mallon killed the game off, netting his maiden league goal for Cliftonville.
"Everyone is telling me it's a penalty,” King told the club’s media channel. “He says it has hit the chest - I genuinely hope he's right.
"I went to speak to him at half-time about it and he was clear on it - that's fine, that's his opinion, but at crucial times I thought he was poor for us.
"He didn't give me anything today and the third goal was clearly offside.
"That's football and I totally accept it, but they seem to have got everything today and the same fouls we weren't getting they were.
"If they are going to be bad or good, it has to be equal.
"I don't mind if they make bad decisions because we all do - I make bad decisions as a manager and coach, but do it on both sides."
Following Glenavon’s victory over Loughgall on Saturday, Carrick now sit ninth in the table, but King felt his side gave everything against Cliftonville, who remain third – five points behind leaders Linfield having played one match more.
"I thought we were decent and at crucial times of the game things didn't go for us,” he added. “They are 1-0 up at half-time when we made the right decision to cut the ball back, but they've broke from poor execution of the free-kick and got plenty of people ahead of the ball when we have plenty in the box.
“We regrouped at half-time and I said to the lads 'pin them in their half and let’s give this a rattle' and I genuinely think we did that.
"We were very good for the first 20 minutes of the second-half and then we give a terrible goal away which was a killer.
"It's absolutely clinical but what I'll say is their smallest player has got between our big centre-halves and he's been strong. That killed the game.
"We had to change the shape to go four at the back and throw big Emmet (McGuckin) on and then they score a third goal which is clearly offside.
"The referee's opinion to my players is different to the linesman's opinion so they haven't even got their story right.
"The game was done at 2-0. We threw people up top and tried to be more direct.
"My boys gave me everything and I thought they gave me a massive reaction at the start of the second-half, but it's (the defeat) disappointing."