The Stanley boss took over following Cook's departure in October but has endured a torrid time and headed into the fixture with one win in 11 League Two matches to his name.
But Rommy Boco's 65th minute strike proved to be the perfect tonic.
"It was thoroughly deserved," said Richardson.
"Our goalkeeper Cameron Belford was Man of the Match but it could have been any one of XI. We haven't got we deserved in some games in December so it was nice to get a win to start the new year.
"January is a big month for us but, at the moment, I am just really pleased for every single one of the players.
"It was weird being in a separate dug out to Paul Cook as I learnt a lot of him when he was manager here and I was his assistant.
"I talk to him every day and have a lot of respect for him. I know the loss will hurt him but, if he had to get beat, he would have preferred that it was us he lost too."