After breaking down in preseason, Ziyech made his much anticipated debut for the Blues in their 3-3 thriller at Stamford Bridge against the Saints.
Ziyech, coming off the bench, tried to make an impact on the game, but Gullit believes the midfielder struggled with the pace and physical demands of the game.
Gullit wanted to see much more from the former Ajax star.
He said on Ziggo Sport via Voetbalzone: "Ziyech does want to take control of the game, but he also has to get used to the high tempo, and how he is now being tackled.
"He thinks he can take the ball on the edge of the sixteen. No, you don't get that time here, they are on top of you."
Ziyech is not the only one who has to get used to the pace in the Premier League, according to Gullit. He draws a parallel with Thiago Alcántara, who made his full debut for Liverpool against Everton on Saturday, which finished at 2-2.
Again, the Dutch great believed Thiago struggled with the pace of the derby.
He continued: "Look at Thiago today, he still plays in a very good team that really accelerates, but he didn't do much in the first half either. You just have to keep it as easy as possible, hit it once, hit it twice. And you have to find that ball behind the defence, gamble on the fast striker."
Gullit played in England for Chelsea before taking charge of the Blues as player-manager. He led the Blues to victory in the 1996/97 FA Cup.
- updated October 19