McDermott was relieved of his duties at the Madejski Stadium on 11th March after failing to guide the Royals away from relegation trouble.
He has since been replaced by Nigel Adkins, a man who was shown the door by Reading's fellow Premier League strugglers Southampton earlier in the campaign.
Zingarevich insists Adkins will be given funds to strengthen the squad he has inherited over the summer and admits he had been hoping to spend in January, with McDermott having been unsuccessful in his efforts to land big-name recruits.
He said: "I want us to be an established Premier League club.
"There is always a budget and I felt the manager should have done more in January.
"We tried to sign some very big players and we were not successful.
"It was a really tough decision to part company with Brian because he was a great person but Nigel Adkins is here now and will get our full backing."