Gunners legend says he is worried about Arsenal's favourites tag, and would have preferred Liverpool as opponents.
Tim Sherwood's Villa side knocked out the Reds on Sunday, winning 2-1 thanks to Fabian Delph winner to set up a final against the Gunners.
Wright told BBC Radio 5 Live's 606 programme that he is taking nothing for granted ahead of the final on May 30.
He said: "You have to be afraid of Villa. Yes they are still down near the bottom of the table but the momentum and the way they are playing they are going to be fine.
"Arsenal would've gone into the Liverpool game on an even keel, against Villa people may view them going in as favourites due to the form they are in, and I'm really nervous of arsenal when they go in as favourites. It makes me worry."
The Gunners were heavy favourites going into their semi-final against Reading yet still made hard work of it, winning in extra-time thanks to a goalkeeping howler.
Last season they needed penalties to beat Championship club Wigan Athletic, and again needed extra-time to beat Hull in the final.
More recently they blew their Champions League campaign losing 3-1 at home to Monaco, a match which they entered as heavy favourites.
Oddschecker currently price Arsenal as 1/3 favourites to win the trophy and Aston Villa 13/5.