Danilo D'Ambrosio emerged hero of the day as his 77th minute strike ensured a 2-1 win for the Nerazzurri at Stadio Giuseppe Meazza.
Mauro Icardi put the hosts ahead on the stroke of half-time before Milan Skriniar's own goal levelled things up for the visitors in the 53rd minute.
“I am pleased with what the team are doing and we are finding the right winning solution," Asamoah, who picked up a 72nd minute yellow card in the full-time appearance, told his club's official website.
"It’s always important to win at home, and not simply due to the goals.
“We are growing a lot. The league isn’t easy and it takes players with a strong mentality during a match.
"Opponents can score but games are played right until the final whistle.
"I try to play my own game and to help the team."
Inter, by the result, tie fourth-placed Fiorentina on point on the league table.
The Nerazzurri return to Serie A action on Saturday with a home fixture against Cagliari.
Asamoah, who joined Inter from Juventus in the summer, has so far made six league appearances for Luciano Spalletti's outfit.
He also has one Champions League outing to his name.