The FC Zurich frontman scored both goals as Der Stadtclub edged Grasshopper Club Zurich 2-0 on the opening day of the championship.
"It was a great start and thank God we won but this is just the first game," Dwamena told KweseESPN.
"Let's see what happens at the end of the season.
"Tony was a great player for Ghana and as a young player, you will definitely have someone to look up to.
"I cannot be like him because I have not reached his level yet. I can only hope to get anywhere closer to what he did."
Dwamena will hope to continue his good form when Zurich host Thun on Sunday.
The centre-foward, who joined Ulrich Forte's side from Austria Lustenau in January, scored a combined 30 goals over the course of last season.
He was once on the books of Austrian giants Red Bull Salzburg, featuring for feeder side Liefering.