Lions coach Warren Gatland stoked the fire on Sunday when he said he thought the All Blacks had targeted Murray during their 30-15 victory in Auckland the previous day to injure him as a way of nullifying his attacking box kicks.
All Blacks coach Steve Hansen disputed the claims, calling them "desperate", while assistant coach Ian Foster said they were just part of the "noise" coming from an under-pressure Lions camp.
Kaino, the player at the centre of the allegations, was peppered by reporters about the incident on Tuesday.
"No, it's never our intent to go out and injure someone," Kaino said several times at a news conference ahead of Saturday's second test in Wellington.
"I guess people have their opinions on it and all I can say is it wasn't my intention to go out there and target his planted foot.
"It's never nice when you have things done to you outside the laws. The way we do things is within the spirit of the game."
Kaino admitted that he was not trying to tackle Murray in the incident which left the Ireland scrumhalf on the ground but uninjured, saying he was attempting to disrupt his kick and simply missed.
"I didn't go in to tackle him. I rolled into his leg. What I was trying to do was... his swinging foot, if you can disrupt that it's like an ankle tap so you can disrupt the kick," the 34-year-old double World Cup winner said.
"My timing was off and I rolled into his planted foot."
Gatland also said he would probably talk to second test referee Jerome Garces about being extra vigilant at Wellington Regional Stadium and Kaino said the All Blacks would also be more careful.
"Obviously, there's more attention being brought to it and it's obviously a strength of the Lions, that kicking game," he said.
"We need to make sure we're on the right side of the law when we do things. I thought I was there, but I'll be a little bit more cautious."
(Reporting by Greg Stutchbury; Editing by John O'Brien)
