The Reds were beaten 4-1 in the Premier League at Etihad Stadium, with domestic action returning following the March international break.
Mohamed Salah opened the scoring thanks to a curling finish in the 17th minute, though Julian Alvarez levelled from close range ahead of half-time.
Kevin De Bruyne then struck just a minute after the interval, before further goals from Ilkay Gundogan and Jack Grealish saw City claim the spoils.
Henderson – who returned to Jürgen Klopp's starting line-up in Manchester – admitted his disappointment at the start to the second period, which saw the game move away from the Reds.
"I think that was a big moment in the match and we didn't react well after the second goal," the captain told Liverpoolfc.com post-match.
"[We] didn't defend it well enough. From then the game sort of ran away from us. In the end we couldn't get anywhere near City. We're disappointed [with the] second half and that decided the game.
"It's very difficult. That's what they’re good at when they go in the lead, they keep the ball away and wait for the right moments. It's really difficult to press and try and win the ball back – from the second goal they dominated the game."
Liverpool now face a swift turnaround ahead of the midweek visit to face Chelsea at Stamford Bridge, which will again come in the Premier League.
"We've got to try to keep going," Henderson added. "There were good moments in the first half. If we're being critical, we probably should go 2-0 up – or at least score a second goal.
"We weren't ruthless enough in either our box or their box, and that's where the game [was] decided really. Overall, a really disappointing day, but the games come round thick and fast and you can't be too down. You have got to try to react in the right way, try to use the positives and try to be better in the things we didn't do well and keep going."