Grayson, 42, was sacked earlier on Wednesday following Tuesday night's 4-1 home defeat to Birmingham, with assistant manager Glynn Snodin and first-team coach Ian Miller also leaving the club.
Leeds dropped out of the top six after three successive league defeats over the Christmas period and Grayson had come under increasing pressure since, with another npower Championship defeat proving the final straw for Bates.
Grayson and some supporters had suggested he was not getting enough financial backing from Bates following the sale of key players Max Gradel and Jonny Howson in recent months.
However, the 80-year-old insists Grayson had all the money necessary, citing the large squad at Elland Road as proof.
"We have to acknowledge the previous three seasons Simon got us to the League One play-offs then promotion and then we finished seventh (in the Championship) and we have backed him all the way," Bates told Yorkshire Radio.
"At 30 players, we have one of the largest squads in the Championship and bigger than some in the Premier League.
"We spent over £12m on wages so why are people blaming me for the recent results?
"All the money we have received has gone back into the squad. The manager decides who he wants to buy, we as the board just pay for it. I only said no once."
Bates believes that a fresh start could see Leeds still remain in the promotion hunt.
"Simon told me in November we were going to win promotion. I am a little bit disappointed he mentioned last night he has been working under financial constraints.
"We are over 30% over budget on players wages. What I don't understand is why we are where we are with what we have spent.
"Since the present system wasn't working we want something fresh.
"Having said that, thanks to Simon, but we have to move on.
"We have got 18 games to go and we can still get into the play-offs but we need a fresh start, fresh look and fresh attitude.
"We are building a club first and a team second and we are making progress when so many people are having financial difficulties."
Meanwhile former Leeds manager and player Eddie Gray has urged the club to appoint a young manager as Grayson's successor after former QPR and Sheffield United manager Neil Warnock emerged as an early favourite.
"I don't know if the club have their mind on anybody," Gray said. "I think they will be looking for somebody youngish but with a bit of experience.
"Everyone has put two and two together because he is available and he has a track record of getting people up. But I don't know if they will go for Neil just because he is available.
"Simon is clever and would probably have known he would be under pressure.
"He is still a young manager and he will get another job and he will bounce back.
"He can walk for the job he has done with his head held high.
"Getting promotion was a great moment and he brought the fans a lot of joy at Old Trafford (when Leeds beat Manchester United in the FA Cup) and there were some good moments for him."