Smith (centre) oversaw a 27th Old Firm victory as Rangers manage
Walter Smith praised Rangers' fortitude after their 3-1 win over Celtic.
Having drawn 1-1 with Champions League opponents Valencia on Wednesday, Smith was delighted his players had produced another strong showing at Celtic Park.
"Everyone's got to be aware that our team are doing very well at the present moment," said the Rangers manager.
"To have a Champions League game on Wednesday night and then to come out and play in this atmosphere on a Sunday, it's not easy."
Rangers trailed at half-time following Gary Hooper's opener in first half injury time but Glenn Loovens's own goal and Kenny Miller's double, the second a penalty, gave the visitors victory.
"I was a little bit disappointed to lose a goal just on the stroke of half-time but I suppose Celtic will be disappointed to lose to a set play just after half-time," Smith told BBC Scotland.
"After that, we had our best spell of the game by far for the next 20 minutes or so.
"Once we got in front we just had to see the game out and we're obviously delighted with that.
"We have to put a lot into each of the games that we play and it's not easy for any of our boys. It's a great win for us."
Both sides had gone into the game with a 100% domestic record and Rangers' win takes them three points clear of Celtic at the top of the Scottish Premier League.
But, ever the pragmatist, Smith is not getting carried away following the derby win.
The referee was close enough to it, I don't think there was anyone impeding him so he was there to give the penalty kick and that's it
"It's a terrific domestic start," said Smith. "I don't think in the period of time previously when I was manager, that we managed to do that. But both teams were going into it with that in mind. We're fortunate that we're the ones that came out on top.
"Anybody who believes that you're nine games into a season and there's any great indication of what's in store in the season, I'd like them to tell me. I might become a wee bit more relaxed if they could tell me one way or another what's going to happen to us."
Smith, who is due to retire at the end of the season when his second spell as Rangers manager comes to an end, said before the match that he will not miss Old Firm games.
"I don't think you can say that you particularly enjoy them during the match," Smith said.
"Sometimes in the aftermath of the game, if you've won, you can but to me, it's not the most enjoyable Sunday afternoon that you'll have."
Celtic's players were unhappy with the award of Rangers' penalty, feeling Kirk Broadfoot had gone down too easily following the challenge by Daniel Majstorovic.
"I haven't seen any of them at all, I've not had time," added Smith when asked if he had seen replays of the incident.
"The referee was close enough to it, I don't think there was anyone impeding him so he was there to give the penalty kick and that's it."
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