Georgios Samaras was the hero for Celtic after his double secured a 2-0 win as the Hoops moved four points clear at the summit of the Clydesdale Bank Premier League, although the Scottish champions do have two games in hand.
The New Year showdown had failed to live up to its billing until Samaras' second half opener sparked the game into life, before he sealed the victory from the penalty spot.
And, as far as Smith is concerned, the nature of those goals was the hardest part to take.
"We've got to be disappointed with the way we conceded the goals, they were poor goals from our own point of view," he said.
"We've got nobody to blame but ourselves in that respect. I'm disappointed that we lost in the manner we did.
"If Celtic had scored a couple of good ones, it might have been easier for us to take."
Rangers appeared to be missing a spark today as they squandered the opportunity to reclaim their lead at the top of the SPL in front of their own fans.
But Smith claims he had no real complaints about the performance of his players, other than in the final third with Fraser Forster barely troubled in the Celtic goal.
He said: "I didn't think there was a flatness about Rangers today. I thought we played very well up until about 25 yards from goal.
"I think you've got to give credit to the opposition at times. I felt Celtic defended very well today, they set their stall out to play deep and not allow us great opportunity to get behind them. That worked very well for them.
"My disappointment is that we didn't do enough to cause them a problem in that respect.
"If you were looking at the game, I thought we started that game as well as any Old Firm game I've been involved in."
Rangers were without Steven Naismith, after he failed to win his fitness battle ahead of the crunch match, but Smith refused to use his absence as an excuse.
"Both sides were missing players today," he pointed out.
"With the way the game was being played, especially in the first half, we should maybe have been a bit better in front of goal.
"We only really had the header that hit the bar in the early part of the game. It was one of those games where we needed to get the first goal to force Celtic out a little bit.
"They sat back and defended very well today and we didn't take advantage of the possession we had, especially early in the game."
Smith handed a first start to youngster Jamie Ness and was pleased with how he coped with the occasion.
"I thought he played very well," he said.
"It was always the case that he was bound to tire because he has only played two or three games recently. He's back to form and I thought he played very well."
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