Matt Targett netted his first goal for the club with just seconds remaining to earn Smith’s men a 2-1 victory on an afternoon when his team were again on the wrong end of VAR decisions.
Adam Webster opened the scoring for the Seagulls after Conor Hourihane appeared to be wrongly penalised for a foul, before Aaron Mooy was sent-off for the visitors.
Hourihane then saw an equaliser chalked off by the video referee after Wesley was deemed guilty of an infringement in the build-up.
Skipper Jack Grealish did level for Villa but the home side laboured with a man advantage until Targett struck at the death.
Smith acknowledged his team were below par but felt the victory made up for past poor fortune, after seeing a string of poor decisions go against them in previous games.
He said: "We probably didn't deserve all three points today but it's three points we deserved in previous games.
“I'm certainly not going to take that away from the lads. Brighton are a very good team, Graham coaches them very well but we weren't very good without the ball.
"The lads clapped Matt into the dressing room for what they thought was a cross. He's not known for goals, that's for sure, but great feet from Jack as everyone knows he's got, slipping him in.
"We were going all out for the winner and they defended resolutely and they'll be distraught as we were last month at Arsenal.
"The squad's full of endeavour. We'll keep pushing and they don't know when to stop, they keep going which is such a good trait to have.”
Villa saw a goal chalked off for the second home game in succession after Hourihane’s strike was, eventually, ruled out following a VAR review, which deemed Wesley to have fouled Brighton keeper Mat Ryan.
Smith said: "Everybody in the ground is celebrating. Brighton are ready to kick off and then, for the first time I believe this season, VAR has got involved in a subjective decision.
“I must have missed the memo during the international period that we were starting to do that.
"It (VAR) takes a little bit of fun out of the game now. The supporters let everyone know what they felt about it. In my experience, it's not been a great one.”