The Hibs boss had riled the Englishman earlier in the week by claiming Warburton had a ‘very easy’ job rebuilding the Ibrox club following its failure to get out of the Ladbrokes Championship last season.
The former Brentford boss responded by saying: “I would suggest any manager without the facts keeps his mouth shut.”
However, it was mostly sweetness and light at Rangers’ Murray Park training ground when he was asked about the issue.
He said: “My job is to always defend Rangers Football Club. If we think something inappropriate has been said then we’ll say our piece.
“It’s gone. We move on from there. I think I made my thoughts very clear.
“I never talk about any other club other than to be supportive or complimentary about the team.
“It’s finished now. I know Alan very well and he knows me. It’s water under the bridge. We’ve spoken before, it will be no problem.”
Asked if it would affect his relationship with Stubbs, he replied: “If we are that childish then I think we’ve both got a problem.
“I’m sure we can rise above that and move forward.
“It’s a competitive industry you’re always going to have your heated moments so to speak.
“They are certain moments when there are raised voices but right now there’s no story.”
In the first game of the season Rangers beat Hibs 6-2 at Easter Road in the Petrofac Training Cup but Warburton is expecting “a tough game against a very organised opponent”.
“Both teams we’ll look at that first game and learn from that,” he said.
“It’s all down to who plays better on the day. Right now we’re in good shape and form. The players are hungry, focused and looking forward to it.
“We’ll look at how they play and where we think they are vulnerable but it’s about us.”
After signing Tottenham duo, Nathan Oduwa and Dominic Ball, on loan last week Warburton revealed he was “very close” to adding another player to his squad.
However, he would not confirm it was 18-year-old Arsenal youth player Gedion Zelalem, who, reportedly, had been in Glasgow to speak to the Govan club.
The Gers boss insists Rangers is an attractive proposition to any prospective signing.
“I think you just need to take one look at the training ground and Ibrox,” he said.
“You put the TV on and see a 50,000 sell-out crowd at Ibrox. The atmosphere, quality of pitch and the stadium means it’s not a hard sell.
“Our job is to find the right players who can deal with that. It’s a certain type of player who can deal with that environment.”