And, at a time when Rangers have been forced to grind out results without several key players, Smith believes Davis has been an inspiration to the entire team.
He said: "Steven Davis has been playing exceptionally well recently and added a couple of goals for us which is great.
"If there is a better player going around in the country then we have yet to see him. He is doing exceptionally well for us at the present moment.
"He has played well for us since he came here, he is a very consistent performer and he has been a big part of our team since he came.
"He has shown in central midfield what he can do and he is a central midfield player more than anything else.
"But, because of our situation in having more central midfielders, he has been asked to go to the right-hand side and it's not affected him greatly.
"He still turns in decent performances and, recently, I think he has been a bit of an inspiration for the whole team."
Pedro Mendes' move to Sporting Lisbon has been confirmed but Smith admitted his search for new personnel before the end of the transfer window has so far failed to yield any positive results.
"We have lost both Pedro and Jerome Rothen and that would free up a little bit of money to get a player in on loan," he said.
"We are currently having a look around to see if we can find someone. We've had no success so far and, if we don't have any, we won't bring someone in just for the sake of it. We'll have to wait and see what transpires."
Meanwhile, Smith believes Kyle Lafferty simply needs a goal to bolster his confidence after again failing to find the back of the net against Falkirk.
The Northern Ireland international has been asked to fill the void left by the injured Kris Boyd but has so far failed to make the most of his long-awaited opportunity to play up front.
"They've got to get a run of games," said Smith.
"It's not easy for Kyle Lafferty or John Fleck to sit out for the majority of the season and then when Kris Boyd and Kenny Miller get injured to have to come in and play.
"It's not an easy situation to put any player in, especially when they're just finding their way as Kyle is at centre-forward.
"He has played far more games wide on the left for us and has scored a number of goals there. He is just going through a spell just now where he needs a goal or two to give him a little lift in confidence."
The result leaves Falkirk rooted to the foot of the SPL and boss Eddie May admitted: "It's a difficult venue and we haven't got a result here [in the league] since 1924 so it's a big ask for any Falkirk team to come here when you look at the history books.
"It was a good free-kick from Steven Davis and he executed it well but we could definitely have done better at the other two goals.
"In terms of playing and moving the ball and trying to create things, it's the best we've done for a while.
"It's not nice coming away from here having been beat 3-0 but that's probably why they are so many points ahead. They are a good team."
Source: Team Talk