A 3-0 win against Grimsby Town gave the Reds’ their fourth consecutive win and leaves them 10th in the table, four points short of the play-offs.
Smith insisted that it was always going to take time for Kewell’s methods to work, but believes that they have made all the difference now.
He said: “We said beforehand how we wanted to make it four in a row but it was made hard, especially in the first half, because it was so windy and the pitch wasn’t the best.
“We got the goal and played our way. We moved the ball around well in the second half and we created chances. We also kept another clean sheet which we are happy about.
“It was always going to take time to adapt to the gaffer’s ways and what he wants.
“We train very hard every single day and we believe in what he wants and that is paying off now on the pitch.
“It’s obviously taken time to come out onto the pitch but I think it’s now showing that we believe in what we are doing with and without the ball.
“It’s everything we’ve been working on within training, everyone knows where they are meant to be and our combination play with the passing is working.”
Midfielder Smith, who’s penalty to open the scoring leaves him as the club’s second leading scorer this season, highlighted the importance of goals coming from all over the pitch and praised the impact of Karlan Ahearne-Grant’s arrival.
He added: “In the role I’ve got in the team, I need to score, I need to assist and I need to work hard.
“Everyone needs to chip in with goals and assists. It’s my role and I’ve got to keep doing it.
“Payney (Josh Payne) didn’t start today so it was me to take the penalty and I was confident and glad that it went in.
“It’s massive (the effect Ahearne-Grant has). He’s a fantastic young player coming from Charlton.
“He’s doing his job, scoring two in two games, and hopefully he keeps doing it.”
Smith believes they must not take their form for granted, with a tough trip to top of the table and in-form Luton fast approaching on Tuesday (February 13).
“We’ve got a tough game coming up on Tuesday and we’ve got to prepare right and hopefully we win,” he said.
“We believe that we can win and we go there for the three points.
“We don’t go anywhere for a draw. Against Chesterfield we scored in the last couple of minutes (to win it) so we believe and we’ve got to do our job.
“We believe in the style of play and if we do that no team can touch us. We are on a good run and we’ve got to keep going.”