Manager Jim Jefferies has been angered by suggestions by Celtic boss Neil Lennon that his Hearts side did not try in the 4-0 weekend defeat by Rangers.
But Lennon has since said his comments about teams not "competing" against Rangers were not specifically directed at the Edinburgh side.
"Should I not accuse him of not trying against Inverness?" Jefferies had said.
"Because it fired Rangers up and it made it more difficult for us at Ibrox on Saturday."
Rangers won their previous league match away to Motherwell 5-0 and followed it up with a 4-0 win over Hearts on Saturday, although Celtic had already relinquished their two-point advantage at the top of the table after losing 3-2 to Inverness Caledonian Thistle in midweek.
Following Celtic's win at Kilmarnock on Sunday, Lennon said teams had not put up enough resistance to Rangers in recent matches.
"What we are looking for is somebody to compete and give Rangers a game," said Lennon.
"There has not been much evidence of that in their previous two games."
Lennon on Tuesday said the remarks were taken out of context by the media in a deliberate attempt to provoke a response from Jefferies.
"You know they have been misinterpreted," said Lennon. "You know I haven't accused anyone of not competing and I haven't accused anyone of not trying.
"I made an observation on the basis of results.
"I said there there was little evidence in the 5-0 and 4-0 defeat, but that's not an accusation, that's more of an observation.
"I'm not the one misinterpreting my quotes. I think it's irresponsible. The people who asked Jim at his press conference knew and were trying to get a reaction from Jim.
"They were not being accurate with their questions.
"Jim is doing a press conference and people are saying Neil Lennon said this and Neil Lennon said that and I didn't say that all."
Lennon did not think he needed to clarify his remarks directly to Jefferies.
"I shouldn't think I have to," he said. "But, if he wants me to, I will."
Jefferies baulked at the suggestion and insisted that his players had been dominating Saturday's game at Ibrox in the early stages.
"We played to try and win the game," said Jefferies. "I thought it was a little bit disrespectful.
"I get on fine with Neil - I have no problems and I'm not out to cause anything.
"Games are hard enough, but it's disrespectful to say my players didn't try against Rangers because that's one thing they did do.
"They gave everything and were the better side for the opening 22 minutes."
Jefferies had several players out injured for Saturday's match at Ibrox and was also forced to make do without club captain Marius Zaliukas at the behest of the club's majority shareholder Vladimir Romanov, who feared the Lithuanian player would be red-carded by referee Iain Brines.
Jefferies insisted that, despite the depleted squad, his players did offer a test, but Rangers and their support had been boosted by Celtic's failure to reclaim the top spot.
"Considering the number of players I had out unavailable on Saturday, I was well pleased with their attitude," said Jefferies.
"Yes, they made mistakes, yes they were overpowered - but Ibrox was as noisy as I've ever seen it and the only reason it was like that was because Celtic handed Rangers the initiative.
"I think it's wrong to accuse us.
"We're not trying hard to win at Ibrox for Celtic and we're not going to try hard against Celtic for Rangers' benefit.
"We're trying to do it for our own."
Zaliukas returns for Wednesday's home game with Celtic, along with first-choice goalkeeper Marian Kello, while Eggert Jonsson is available after the club launched an appeal against the red card the defender was shown at Ibrox.
Meanwhile, Motherwell manager Stuart McCall also dismissed the comments attributed to Lennon.
"If anyone thinks I want to send a team out to get beat by anyone, obviously they don't know me," he said.