Jurgen Klopp's side are favourites to reach the last four of the Champions League after seeing off their domestic rivals in the first leg of their quarter-final tie.
Liverpool scored three goals in the opening half before defending resolutely after the break, giving them a sizeable cushion to take into next Tuesday's second leg in Manchester.
Oxlade-Chamberlain, who made it 2-0 with a long-range strike beyond City goalkeeper Ederson, admitted the home support was "unbelievable" – and not just during the game.
"It was a great start for us – going 3-0 up before half-time set us up brilliantly," the England international told BT Sport.
"We knew we had to start fast, but I don't think that was hard today with the atmosphere. From coming into the ground right through the warm-up, the fans were unbelievable out there.
"It got me going and I'm sure it got the rest of the boys going. We've won the game in the first half and then had to defend well in the second."
The England international found the net for the second time against City this season at Anfield, having also scored from distance in Liverpool's 4-3 Premier League triumph back in January.
"It was a good strike. The space just opened up for me," he added. "I've been working on that, on trying to do it more often. I showed myself that if it's on more often I can keep doing it."
Captain Henderson admitted the players were keen to capitalise on the energy inside the ground prior to kick-off.
City's team bus was damaged by projectiles on their arrival, an incident that led to the Merseyside club issuing a public apology, spoiling an otherwise memorable occasion at the famous stadium.
"We knew the atmosphere would be brilliant, and it was. We had to make the most of that," Henderson said.
"We were on the front foot, [playing at a] high intensity. In the second half they obviously came at us a bit more and we dropped deep at times, which we didn't really want to do, but we defended brilliantly.
"It's only the first leg, so we need to make sure we do it again away."
0 - Manchester City failed to direct a single shot on target in a game for the first time since 26th October 2016 (v Man Utd in the League Cup). Blunt.— OptaJoe (@OptaJoe) April 4, 2018
However, Henderson will miss the return fixture at the Etihad Stadium after picking up a booking for a foul on former team-mate Raheem Sterling in the closing minutes.
"I felt as though I could win the ball. I thought Raheem hadn't really seen me, but he got there first," he said.
"He [the referee] gave me a booking, but I was a bit disappointed because I hadn't conceded many fouls during the game.
"But we've got a great squad and I'm sure we can go there [to the Etihad Stadium] and put in a good performance."