Celtic boss Gordon Strachan conceded afterwards that a third consecutive championship would now be extremely difficult to achieve for the Hoops.
He said: "It's always easy for people on the outside to say these things, isn't it? It doesn't count for anything what anybody else says.
"It was important for us to get a result today in the sense that we still have two visits to Celtic Park, which are going to be tough for us.
"We just have to try to keep winning. We are obviously in a far better position than we have been in for the last few seasons.
"But there is still just less than a quarter of the season to go and we know we have a lot of work to do to improve on the situation we are in at the present moment."
Smith paid tribute to the player who has recently returned from injury to play an important role for Rangers.
"It was a terrific goal and it gave us a lift going into half-time," said the Rangers boss.
"He has been back for a few weeks now from a double hernia and I feel he is a terrific player. I really like him.
"He is a boy who can really impose himself on a game. We have been a bit unfair to him and not played him an awful lot in what I consider to be his best position.
"He has the capability of playing anywhere in the midfield and he has shown that in the last few games."