Two goals from Nacho Novo and a Barry Ferguson strike allowed Rangers to move level on points with their Old Firm rivals in the Clydesdale Bank Premier League, suggesting this year's championship race could go all the way to the wire.
"There was a good level of determination from everyone today and that was important because I felt we had dropped in terms of that in certain league games this season," Smith said. "We will have to show a consistency on that level. Today we managed to get back on level terms with Celtic but you have to remember that is all we have done.
"It was a chance to show that we could come up against Celtic and match them.
"It was going to be awkward for us if we had lost that game today because Celtic would have gone six points ahead of us.
"We were delighted to win and I think we have shown we can match Celtic on a one-off game. Whether we can match their consistency over the period of the season is the biggest challenge for us."
Smith is satisfied with how the opening quarter of his first full season has shaped up so far.
"Not having a great deal of stability in the team and trying to form a team and trying to win every game that we play is a difficult thing," he said. "And playing in the Champions League as well as our own domestic competition is asking a lot of a first-year team.
"As long as we can keep within touching distance until the New Year period we will be delighted. We have some obvious improvements to make as a team and we will continue to try to do that."
Celtic boss Gordon Strachan is refusing to look ahead to the midweek Champions League game against Benfica in Lisbon until he has come to terms with events at Ibrox.
"The better team won because when they had their chances they took them and we didn't," he said.
"They were better at close contact as well, something that our boys who are new to the derby games will have to learn.
"That will be a fantastic experience for these guys and they know fine well that to survive in the football world in Glasgow you have to be able to deal with that.
"It's a lesson today for the guys who have never played in a derby game before.
"I think one or two were surprised by the nature of the game. Maybe we didn't emphasise that more but I'm sure we did mention that it might get a bit tasty!"
He added: "The yardstick is that we are on level points. We have had an experience and it wasn't a good experience but the fact is that we still have the same number of points.
"There is a long way to go. I don't like what has happened but I will have to deal with it and so will the players."
