The 35-year-old stopper believes that it was the Rossoneri's tactics without the ball that led to their triumph.
"We made a big performance, we showed a big sacrifice and spirit," Abbiati told Sky Italia.
"We won a big match against a big team. We knew the ball possession would be with Barcelona, but with the coach we prepared a good match, and thanks to our forwards, who also helped on defence, we gave a good performance.
"Congratulations to the team."
The return leg takes place at the Camp Nou in three weeks' time.