Neil Lennon told Walter Smith to mind his own business after the Rangers boss criticised Andreas Hinkel and the rest of the Celtic side following the Ibrox side's 2-1 defeat at Parkhead.
Hinkel had claimed before the game Celtic were a better side than the Clydesdale Bank Premier League champions.
Goals by Lee Naylor and Marc-Antoine Fortune gave the Hoops their first win of the season against the Light Blues who scored through Kenny Miller and had Lee McCulloch sent off near the end after picking up two yellow cards.
Afterwards Smith hit out at Hinkel and claimed Celtic had been a poor set of professionals before Lennon took over from sacked Tony Mowbray in March.
Hoops' interim boss Lennon said: "It's not Walter's place.
"He's not the Celtic manager and he has not affiliated with the club so those comments should be best left to someone at this club.
"Did I not make things clear after (the defeat to) Ross County?
"It was my place at the time and I asked the boys to prove me wrong and they have gone a long way to doing that.
"But I don't comment on Rangers, I never have done, certainly not as a manager anyway.
"I have been quite gracious abut Rangers, their performances and the way they have dealt with things.
"So I don't think it's Walter's place to criticise the Celtic players, he should leave that to people like myself."
The former Celtic captain claimed it had been "horrible" standing on the sidelines in his first Old Firm games as Hoops boss but admitted the victory meant more to him in his new role.
He said: "It probably meant more to me as a manager than a player.
"I didn't want a draw, I didn't want to get beat, I wanted a win and that's what I asked them to do at half-time, just win the game.
"It got a bit hairy at times, Old Firm games are quite like that.
"When you go a goal up subconsciously you drift deeper at times but it was a magnificent effort.
"I could see the goal coming for Rangers but the response was magnificent, to get the goal just before half time was great.
"It's not fair to single players out though, they all made massive contributions.
"I wanted to get them in at half time and settle them down.
"But it was hugely satisfying, a big three points, and some big performances from a lot of players, beating Rangers for the first time in a while.
"That was our cup final tonight, against a very good, very dangerous Rangers team and we won the game so I can't ask any more from them."