Villa are currently at risk of relegation, despite securing a place in the EFL Cup final on Tuesday, sitting just two points clear of the drop zone with 14 matches still to play.
Judge spent three years under Smith at Brentford and when asked about the Villa manager's style of coaching, Judge was full of praise.
"I worked well with Dean before I broke my leg and as a person I got on really well with him," Judge told Tribalfootball.com.
"He is an easy man to talk to and he likes playing proper football, so I really enjoyed my time under him.
"Villa are struggling at the moment but they brought in a lot of players over the summer and it takes some time to gel.
"I have seen them play a number of times this season and they have had some unbelievable performances and I think Dean has got a good coaching staff behind him, so I think they will stay up."
Villa had to make large scale changes to their squad over the summer with a number of the players that helped them earn promotion leaving or returning to their parent clubs.
The club have made 14 signings already this campaign in an attempt to bolster their squad, while they have also seen Tom Heaton and Wesley suffer season ending injuries.
After Saturday's loss to Aston Villa, the Midlands club are teetering one point above the relegation zone.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!