Still, 62, earlier this week ended a nine-year stay at Victoria Road, his second spell in charge of the club, and brought an end to a reign which had seen him become the fourth longest-serving manager in the country behind only Sir Alex Ferguson, Arsene Wenger and David Moyes.
Still had taken the Daggers from the Conference to League One and back to League Two again but opted for a fresh challenge back in non-league football at Luton, with unconfirmed reports suggesting he has penned a bumper contract at Kenilworth Road.
Dagenham, in an official statement on Tuesday, admitted that their initial shock and disappointment had been replaced by respect for Still's wishes and all he had done for the club, with the powers-that-be at the Essex outfit even waiving significant compensation in favour of a nominal fee to allow Still to make the move he desired.
And managing director Thompson said: "John goes with our best wishes. He definitely built upon the work that Ted Hardy and Garry Hill had done previously and he took us to a different level, the likes that we'd never seen before.
"We're disappointed that he's decided to go but we wish him well."
Thompson added: "I and the board took the decision that, after everything he had done for us, it would be...what's the right word?...immoral maybe, to hold him against something that he wanted to do.
"I've known John for 30 years and Monday was hard. One side of me knows we've got a manager we don't want to lose; another side of me knows there's a lot of money there at stake which we could well have done with, but equally you've got to respect a man who has done what he's done for us but now feels it is the right time for a new challenge.
"We'd already said we would give John a testimonial game and we've agreed to keep that even though he's left us. It wasn't supposed to happen for another two-and-a-half years so no plans have been made for it!"
First-team coach Wayne Burnett has taken the reigns on an interim basis until the end of the season and will be in charge for Dagenham's League Two match at Bradford on Wednesday night.