The wing ace helped Villa blow away the Toffees as they scored three goals in the space of nine second half minutes.
Bailey, who joined in a £25million switch from Bayer Leverkusen last month, completed the scoring with a stunning strike on his first Villa Park appearance.
Smith said: “He (Bailey) is one who is going to be a crowd favourite, that is for sure. He has great ability, showed great delivery from a set piece and scored an excellent goal too.
“He gets bums off seats and that is what supporters at this club want to see.”
After a relatively even opening hour, Villa took the lead when Matty Cash finished a neat move by thumping home his first goal for the club.
Lucas Digne then headed Bailey’s corner into his own net before the Jamaica international blasted home, after latching on to Danny Ings’ through ball.
Bailey was forced off with a tight quad soon after but the injury is not thought to be serious.
Smith continued: “I thought they were very good goals. Very well worked goals too. We probably had an edgy spell for five minutes before we scored the first goal.
“My message to the players at half-time was our outside centre-halves never really broke the lines with the ball enough. In the second half we did that a little better.
“They had a spell of pressure for five minutes before we scored and that made everyone a little bit edgy but the goal lifted the roof off.
“I thought 3-0 probably flattered us but after the goal went in it was all guns blazing.”