Ziyech was one of the players most widely criticised following Saturday's defeat at Manchester City and the Moroccan, who was making only his eighth league start of the season, had a point to prove at the Amex Stadium.
He gave the visitors the lead against the run of play with a speculative shot from outside the area but barely reacted after hitting the net despite being mobbed by his team-mates.
"This is what you play for," Cole said on BT Sport. "He's a fantastic talent, he hasn't hit the ground running in the Premier League as it's very different to the Dutch league. But the not celebrating... It doesn't sit well for him as a lad.
"If he was in my team I'd be saying come on. You know when lads are not happy and they're not playing. But if I come off the bench and score a goal, it's a release of energy."
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