Bain, chief executive of Silverstone's leaseholders Octagon Motorsports, stepped down on Monday.
Ecclestone described Sunday's Grand Prix as "a country fair masquerading as a world event".
The remarks came despite major road improvements which prevented a repeat of traffic chaos around the Northamptonshire circuit in recent years.
But Bain responded: "The feedback from the customers has been healthy. That's what matters rather than the opinion of one man."
However, Octagon released a statement on Monday in which Bain said: "I have had a tremendous few years and I am very proud of the Grand Prix that we staged this weekend.
"It is disheartening still to hear gratuitous outside comments about the event, and I do not wish them to overshadow what the team has achieved."