The veteran keeper spoke of his man-of-the-match performance in Wednesday night's game, and hopes that his side can embark on a good run of form
The 35-year-old goalkeeper pulled off a string of wonderful saves to keep his side in the match and was glad that he could help his team to a win.
Speaking in a post-match press conference, Abbiati said: "It was important to get a result here and that’s what we did.
"My second half saves were important for how the match finished. My most difficult save was the one from Hulk's free kick. He hit the ball very hard and my arm still hurts from the shot.
"I was happy with the win and that was why I celebrated like I did. It’s tough to win away from home in the Champions League and we did it."
Having joined the Italian side in 1998, Abbiati has had his critics over the years but he revealed that he is not fazed by what others say about him.
"I don’t read the papers whether I’m playing bad or whether I’m playing well. If I’ve been with the club as long as I have there must be some reason why. It was a team win tonight."
Milan look to get their Scudetto charge back on track when they entertain fierce rivals Inter on Sunday and Abbiati is looking for a strong response from the side.
"It would have been nice to get three points against Parma and there’s bitterness about that because we played a good game and we only conceded the goal on the free kick," he said.
Stephan El Shaarawy scored the pick of the goals in the victory against Zenit and Abbiati is convinced that the 19-year-old striker has a bright future at the Giuseppe Meazza.
“We’ll be thinking of the derby from tomorrow. El Shaarawy is a great player. He’s young and has a lot to show but he’s got the quality," the shot-stopper said.