Wigan Athletic boss cites debt of gratitude
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Cook resigned his post shortly after Latics were relegated to the third tier in 2020 after being placed into administration by the former owners.
But Richardson says his involvement with Latics - for whom he spent two spells during his playing career - didn't end there.
"I had a lot of success with Paul, we had a lot of success together," said Richardson, who remained with Latics after Cook's departure in order to, in his own words, 'bring some sanity to the situation'.
"He's been on the phone most mornings, getting me up and down that M62, and he was probably the first person to send me a message at full-time after the Shrewsbury game.
"If Chesterfield hadn't had a game on the Saturday, he would probably have been there in the stands with us.
"He had this football club in a fantastic place, touching the play-offs in the Championship.
"And there was nobody more hurt than him when what happened happened.
"But he takes a lot of credit for this, because I picked up a lot from him, having worked alongside him for so long.
"I'd like to think we supported each other very well during our time together, and now it's my time to support him (at Chesterfield)."
Latics were the busiest movers in the transfer market last summer after only having a handful of senior players on the books.
While it's not expected to be quite so busy this time, Richardson says work is already under way ahead of next term.
"In this industry, it's never too early to be looking at next season," he said.
"They're probably already talking about it, planning, working out what we're going to do.
"You always silently go about your work, but the preparations have already begun."
Cook and Chesterfield face FC Halifax in the National League play-offs as they bid to return to the EFL.