Richards, who was Vale's top scorer for four successive seasons, played a major part in goals for Jay O'Shea and Tendayi Darikwa as Cook's side strode to a fourth straight win in impressive fashion.
Vale remain in second place, but on the day they were a clear second-best as Chesterfield debutant O'Shea and Mark Randall ran the game behind lone striker Richards.
Cook said: "Rico played very well. He's a strong boy who mixes his game up well and he was the catalyst to a very good team performance.
"He holds the ball well which enables us to get up the pitch and that was very important. You can talk all day about systems and playing one forward, but we are a very attack-minded side and we get players forward.
"We respected Vale like we do all our opponents, but we didn't fear them.
"They are a strong team who are going well, but we came here to take them on toe to toe.
"We had really effective players throughout the team and I was delighted with all of them.
"We were disappointed to go out of the FA Cup at Tranmere last week, but the boys trained really well during the week.
"We are on great run, but a week is a long time in football. We will just take things game to game."