Liverpool's 10th straight league victory carried them to 77 points, five points ahead of Chelsea - who play Swansea in the late kickoff - and crucially seven points ahead of City who have two games in hand on the Merseyside team.
Liverpool have four games to play and if they win them all will claim their first top-flight title in 24 years.
"That was a remarkable performance," Rodgers told Sky Sports. "I thought we were incredible today. I think the world watching that will see a team with so much spirit, so much quality."
Martin Skrtel then nodded in his seventh goal of the season in the 26th minute to double their advantage.
As a fourth 2-2 draw in the last five games between the two sides looked the most likely result, Philippe Coutinho capitalised on a Kompany miskick to seal the win.
"We totally controlled the game. At halftime we were 2-0 up and it could have been more," Rodgers added.
"Congratulations to Man City because at 2-0 down we were incredible in the first half. You expect a 15-20 minute spell in which they get back into the game.
"They (Liverpool players) showed the character (we have) in this group...to come back and get composure again and score a brilliant goal and get three very valuable points."
The club paid a fitting tribute on the weekend of the 25th anniversary of the Hillsborough tragedy in which 96 Liverpool fans died at an FA Cup game against Nottingham Forest, and Rodgers admitted his side used it as motivation.
"There's always an emotive side especially around this time. Going into the game a lot was made about would it affect the players. We live with it every day.
"The families and victims of Hillsborough are with us every day. It was an inspiration for us rather than something that was going to hold us back."
The affects of the occasion and a draining game played at breakneck speed were plain to see. Liverpool captain Steven Gerrard had tears in his eyes at the final whistle and was visibly emotional in his post-match interview.
"I'm emotional but we need to keep calm," he said. "We still have four big games to come but that meant so much, especially when they got back into the game. You fear the worst at that point.
"That was the longest 90 minutes I have probably played in. It felt like the clock was going backwards during parts of that game.
"We want go all the way. Nothing's won yet but that was probably the biggest statement we've made so far."
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- Vincent Kompany