The Northern Irishman was frustrated by Killie’s tactics as they held out for a 0-0 draw on Wednesday, claiming his team would have found it hard to break down “11 firemen that deep on a pitch”.
Clarke hit back at his Parkhead counterpart, insisting it was not his job to make life easier for the Ladbrokes Premiership champions.
The Kilmarnock manager said: “If you look at the majority of what Brendan said, it was correct and proper - but that (firefighter) line wasn’t really befitting of a Celtic manager.
“It wasn’t so much disrespectful, it was just a silly line to use in what was quite an honest post-match analysis of the game.
“We don’t have to go there and play the way Celtic want us to.
“We went there to play the way that is best for us to get a result. It’s my job as a manager to set my players up in a way that gives us the best chance of getting a positive result and that’s what we did.
“If you are the team with 73 per cent of the possession then it’s what you do with it that counts and on the night Celtic didn’t do enough.
“They only had one shot on target, which for that amount of possession I’d think would be disappointing for Brendan and his team.
“If he wants to insinuate that Celtic could not have broken down 11 amateur players, which is what he was insinuating, then I think he underestimates his own abilities as a coach and the ability of his players because I’m pretty sure Celtic would beat 11 firemen.
“I didn’t see Brendan after the game, we didn’t have the usual post-match chat so I don’t know if he was frustrated or not after the results we’ve had against them this year.
“I don’t think he should be too frustrated seeing as they have two trophies in the bag already and the chance to make it three next week.”
Clarke’s side round off a remarkable campaign when they host Hearts on Sunday.
The Ayrshire outfit were rock bottom when the former West Brom and Reading boss was appointed back in October but they are now guaranteed to finish fifth.
“When I came in originally, I thought we’d be involved in a relegation fight at this point, so to be where were are, to be competitive with all the teams in the top six has been great,” he said.
“But the players deserve all the plaudits. Maybe I’m the one who sits up here getting all the praise because I spend more time in front of the media.
“But the players deserve the credit as they have been fantastic. Hopefully on Sunday we can give the Kilmarnock fans a good finish to the season.”