Williams was sacked along with chief executive Martin Goodman by Baggies owner Guochuan Lai following the club's 3-0 defeat to Chelsea on Monday evening, which kept the West Midlands club at the bottom of the Premier League table.
The former chairman, who was appointed when Lai took ownership of Albion in 2016, has described the "odd feeling" of leaving the club.
"It is an odd feeling, it's certainly unusual," Williams told The Times. "We had gone through a managerial change but it's a results-based game and I accept my part in that. As top of the managerial tree, you have to take responsibility.
"It has been a challenging job but I felt we had done well in the time I was here until this season, and I have enjoyed it.We didn't get the bounce we hoped for when Alan [Pardew] came in and are well short of his usual average points per game, but I think we are now heading on a really favourable run of games.
"I believe in Alan and the squad and I wish them well and really hope they stay up. I believe it will be a fight until the end."
The defeat to the Blues left West Brom seven points adrift of safety in the top flight.