Anwar El Ghazi’s sublime strike saw Villa edge a pulsating encounter 2-1 at Goodison Park.
The victory was just their third in 12 matches but the performance an undoubted return to form, with the victory enough to lift them back into the top half of the Premier League.
And though it might be too late for Villa to mount a charge for European qualification, Smith felt his players had proved a point.
He said: “The attacking intent pleased me most, particularly against a good team like Everton.
“When you look at the team and give players marks out of ten, I don’t think anyone was under a seven tonight and that makes a really good team performance.
“It is easy to say we have nothing to play for or the players aren’t showing much desire. I think they showed that desire today.
“We have been inconsistent over the last two or three months. We have lost a very good player in Jack Grealish and had to find a different way of creating that spark. I think the last two games have shown we can do that.”
Smith also reserved praise for Ollie Watkins after the striker capped a brilliant all-round display with his 13th Premier League goal of the season.
The club record signing fired Villa in front on 13 minutes and was then twice denied by goalkeeper Jordan Pickford after Dominic Calvert-Lewin had headed the hosts level.
“It was certainly (one of his best performances),” said Smith. “We paid an awful lot of money for him but I knew what he was like and how he is as a person, that he would want to grow and keep getting better.
“I thought he was outstanding. He pickpocketed the defender well to score his goal and Jordan Pickford then regained parity with some of the saves he made.
“I think his game has got better. He is a lad who used to beat himself up an awful lot if he missed chances but he gets over it a lot better now and that is the sign of a good player.
“It is something we wanted to work on. We were better on the transition today and our build-up was an awful lot better as well.
“I thought it was a very entertaining game between two evenly-matched teams and I thought we created the better chances in the first half.”