The game ended in a thrilling 2-2 draw, Rodgers' side twice coming from behind, and keeper Simon Mignolet proved their hero in the shoot-out, which ended with Liverpool on top 3-1.
Stevan Jovetic put City in the lead on a couple of occasions, continuing his bright pre-season form, but England internationals Jordan Henderson and Raheem Sterling replied to send the game into penalties, with the result putting Liverpool top of Group B ahead of Saturday's clash with AC Milan.
"I thought it was an excellent game for a pre-season game. It was very competitive and the atmosphere was fantastic so it was a great game for us at this stage of our preparation," Rodgers told Sky Sports News.
"Simon is a wonderful shot stopper, he's made a couple of great saves, but across the team I thought (in the) second half we were excellent.
"We played a diamond in the first half, just to have a look at that and refresh our positioning from last season, and then we played 4-3-3 in the second half and obviously the players are more accustomed to that.
"Raheem Sterling came on and I thought he was outstanding - he's very direct. he's quick - and Jordan Henderson made some great runs to get in. We got two goals and maybe we could have had a couple more. Joe Hart has made a couple of really outstanding saves and all in all I am very happy.
"It was a great game; Manchester City are a wonderful team and they'll go close in the Premier League again this year. At this moment of pre-season, it was a great game for us."
Rodgers also felt Liverpool were slightly unlucky in the goals they conceded to Jovetic.
He told the club's website: "I thought they were unfortunate. Jovetic is very bright, he is alive in the box, he just nicked in and it was unfortunate with the first goal that it was deflected off Stevie (Gerrard).
"His second goal was something similar. We have to also respect the quality that we're playing against - they are a top side. We played very well; we conceded a couple of goals, but so did they."