Rodgers' side led three times in the 3-3 draw in Glasgow, but ultimately had to settle for a first point in Group C.
Having opened the competition with a 7-0 defeat in Barcelona, they ended City's 100% start under Pep Guardiola.
"Tonight is hopefully a good marker of how much the players have improved in a short space of time," said Rodgers.
"But I know there is a long way to go in terms of where we want to be."
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The hosts led twice in the first half, through Moussa Dembele and a Raheem Sterling own goal.
Fernandinho's strike brought City level for the first time, and Sterling showed composure to net the visitors' second.
Dembele re-established Celtic's lead soon after half-time, but Nolito ensured both sides took a point.
Former Liverpool manager Rodgers described his side's performance as "great".
He added: "We felt we could have won but we're happy with a point. Collectively, we were outstanding.
"I'm sure Pep will recognise that it was really difficult night for them. They are a top-class team with a top-class manager, who has coached them really well.
"But how our players pressed the game and forced Man City into mistakes was a great credit to my team."
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Rodgers acknowledged Celtic could have defended better for City's second and third goals, but preferred to highlight the positives from the overall display.
Dembele's two goals took his tally to seven goals in his past six games, and 12 for the season.
The 20-year-old, who joined the club in the summer after leaving Fulham, opened the scoring with a deft flick with his chest, and put the hosts 3-2 ahead with an acrobatic finish with his back to goal.
"We're very fortunate to have him," Rodgers said. "He's been like that since he's come in. He really bullied the Man City back four but he's more than that.
"He's got a wonderful touch. You saw his agility for the third goal. He's got power, he's got pace and now he's a huge talent. He was outstanding."
Rogers also praised Celtic fans for their "absolutely amazing support".
"It's a noise I've never heard before since I've come up here," he added.
Celtic boss Brendan Rodgers believes his team's Champions League draw with Manchester City underlines how much they have improved since his arrival.