The versatile midfielder, who played on the left flank for Inter picked a yellow card after colliding with Frankfurt's Gacinovic in the 25th minute.
Asamoah has now picked up two yellow cards and will miss the game at San Siro next week.
Even though, the Ghana international is disappointed he will be missing the game, the 30 year-old remains confident of his side's chances.
"It was a tough match, It wasn't easy to play in this atmosphere tonight," Asamoah said, as reported by his club's official website.
"We had good chances in the first half, while they were more attacking in the second half and we struggled to keep possession.
"0-0 is a good result that allows us to fight for qualification at home.
"Unfortunately, I'll be suspended for the return leg but I have full faith in my teammates."
Inter held Frankfurt to a goalless draw in the first leg at the Commenzbank Arena in Germany.