The 29-year-old moved to the Hawthorns in a club-record deal on transfer deadline day and took just 20 minutes to open his goalscoring account against his former employers, on the way to helping West Brom to a 3-0 win.
Sessegnon, who scored 17 goals in 87 appearances for Sunderland, volleyed home after Nicolas Anelka had been denied by goalkeeper Keiren Westwood, but he decided not celebrate his debut strike.
"I don’t know if it was inevitable," Clarke said. "But you know that if you play somebody against their former club and their job is to create chances and score goals then there is a strong possibility that will happen.
"He did what we brought him here to do. He is clever on the ball, bright, an entertainer and has goals in him too. It was a very pleasing debut for him.
"I think he showed good respect to the Sunderland fans. They loved him as a player and in his own way he is an engaging character.
"He decided not to celebrate so that’s fine with me. If he wants us to celebrate more than him, I'd be happy with that every week."
Morgan Amalfitano secured the three points in injury time with his first West Brom goal, after Liam Ridgewell had struck in the 76th minute, and Clarke was delighted with the Frenchman's overall contribution.
"I said when we brought Morgan to the club that he might surprise one or two people," the 50-year-old added.
"One of the reasons we brought him in was because his assists record in the French league is good and he had a hand in both goals today, especially the second.
"And he got the added bonus of scoring at the end too. I'm pleased because to have a home debut like that is really good and I hope he can live up to it in the future."
