Hoops defender Andreas Hinkel had claimed before the game Celtic were a better side than the SPL champions.
Smith fumed: "Andreas Hinkel said in the paper the other day that Celtic are the better team.
"If he sits down and he analyses what he said then you've got to say why does he think they are a better team than Rangers when Rangers have won six trophies over a three-year period and reached a European final and Celtic have won two.
"He must feel then, that if they are the better team, something is wrong. It might be if they had shown the same attitude as they showed in the first half of the game tonight, they might have been in a far better position.
"He has got to ask himself that question. If he sits down and says that Celtic are a better team than Rangers, he should ask himself if he's proud of the way they have played over the last few seasons because I'm certainly proud of the way my team has played and my team has something tangible to show for it at the end.
"I can't understand why any professional doesn't take a good look at himself first before saying Celtic are a better team than Rangers because it's patently obvious that they are not and haven't been.
"Maybe it's simply because of their approach and their attitude to the game, that Neil Lennon is now bringing out in them. But if it takes a manager to bring it out in you, then you are looking at a poor set of professionals."
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.
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."