The Ghanaian has been one of the Nerazzurri's top performers in pre-season so far, an amazing midfield display against the Premier League giants in the International Champions Cup his latest exploit.
He joined Luciano Spalletti's outfit earlier this month from Juventus, where he spent most of his time as a left-back or a left-wing-back.
“He [Asamoah] has great personality and individual technique,” Bergomi said on Sky.
“He knows how to protect the ball too and the play starts with him.
"He was a surprise even for me, in a role he hasn’t played for some time now.”
Inter manager Spalletti was first to praise Asamoah's outstanding performance against The Blues.
For goalkeeper Samir Handanovic, Asamoah, together with the other new acquisitions, is doing just fine so far.
"How are the new signings settling in? They’re all good players and they want to learn, there’s been a good feeling from the start," the shot-stopper said in a separate interview.
"I knew Asamoah in Udine, [Stefan] De Vrij is a smart lad and he immediately felt comfortable with us.
"Our aims for the season? Everyone plays to win trophies."
Asamoah is expected to see some action again when Inter face French giants Lyon in their next pre-season game on Saturday.
It will be the 29-year-old's fifth appearance for his new side.