The 3-0 win over the Baggies - Villa’s first at The Hawthorns since 2008 - saw them climb to ninth in the table with two matches in hand on many of the teams above them.
But despite his team winning seven of their 12 fixtures so far - and five out of six away from home - Smith is keeping his feet on the floor.
Asked whether he was now thinking about European football, the Villa boss quipped: “With the pandemic I am not thinking about Europe at all, as we can’t travel at the moment!
“But no, seriously, we are not thinking of it. We are just thinking of the next game.
“There is a great focus from our team at the moment and there is a willingness to keep progressing as a club and as individual players.
“As long as I have got that whatever will be, will be. We will just keep working hard.
“I am really pleased just to see the spirit in the team. I didn’t need to make a substitute, which I like to do when I feel I can rest someone.
“At the moment I can’t give the players enough credit, from the back to the front. That is our seventh clean sheet out of 12, which is really excellent.”
Smith hailed Villa’s performance as they brushed aside the Baggies to record their second derby success in the space of nine days, following a 1-0 win at Wolves.
In front inside five minutes through Anwar El Ghazi, Villa were in control even before home skipper Jake Livermore saw red for a reckless challenge on Jack Grealish.
After attacking relentlessly through the second half, the visitors got their second when Bertrand Traore netted his first Premier League goal for the club before El Ghazi bagged his second of the night from the penalty spot.
Smith said: “I thought it was an excellent performance from start to finish. We wanted to negate the new manager bounce that teams can have and I thought we did that really well.
“We started the game well and got a great goal to start with, one wide player crossing to another wide player.
“I can’t remember them having a chance to be honest, such was our control of the game. It took us a while to get a second but we had control of the game throughout.
“I had never been too worried about the Burnley game, where we drew 0-0. We controlled that and had 27 attempts.
“I knew if we had as many attempts tonight we would be scoring goals and so it proved.
“On Thursday night against Burnley the chances were falling to Bertrand and El Ghazi and tonight they were the ones scoring goals.”