Aston Villa sacked Smith on Sunday after three years in charge following a run of five successive Premier League defeats.
Smith took over Aston Villa in October 2018 following the sacking of Steve Bruce, and the former Brentford manager quickly guided the club back to the Premier League at the first time of asking via the play-offs.
The 50-year-old helped Villa retain their top flight status in their first season back and improved with an eleventh place finish last term.
However, the departure of Jack Grealish to Manchester City in the summer has seen them struggle, with new signings Emiliano Buendia, Leon Bailey and Danny Ings yet to really get going.
'To be appointed the head coach of Aston Villa, the club I supported throughout my childhood, was and remains something I am extremely proud of,' said Smith, via a statement from the League Managers Association.
'Having led the club back to the Premier League ahead of schedule and at the first time of asking after three years in the Championship, the next challenge was to help overhaul the squad and create a group good enough to survive that all-important first season back in the Premier League.
'In doing so, I believe those achievements allowed the club to accelerate its ambitions to become an established Premier League club.
'My belief was that we would continue our progression this season. I understand the football industry and of course, I respect the owners' decision, but I felt that with important players soon returning to full fitness we would achieve a top-half finish.
'One of my roles as head coach at Aston Villa was to improve individual players to enhance on-field performance for the team.
'Playing a part in developing a player who would be transferred for a British record transfer fee, along with creating a pathway for a thriving academy, are all areas in which I feel I've more than contributed.
'I would like to express my gratitude to the owners, Nassef Sawiris and Wes Edens, in giving me the opportunity to manage this special club.
'I would also like to thank the CEO, Christian Purslow, with whom I enjoyed an excellent working relationship as well as the two sporting directors I worked alongside, Johan Lange and Jesus Garcia Pitarch.
'To the coaches, staff and players, my sincere thanks to each and every one of them.
'Finally, to the Aston Villa fans who showed me nothing but love and support from my first day in the job to my last, a heartfelt thank you from my family and I.
'The Aston Villa board's aims and ambitions are to take our club back into European football and I would love nothing more than seeing the club achieve that.
'I've always said that I was simply a custodian of this great football club, and my aim was to leave it in a better place than I found it. I believe that together we have achieved that. UTV.'
