Enzo Maresca's side maintained their 100 per cent record with three second-half goals, scored by Haaland, Jérémy Doku and Rayan Cherki. The result came in Manchester City's first match since the verdict in the Premier League's financial case, against a hostile Anfield crowd.
Haaland said the atmosphere and the team's response had created a memorable occasion for the players and supporters.
“It's part of City and every single fan,” he said. “It's a lovely moment that will stick with us for a long time, when it comes to the feeling of after the game and in the game.”
The Norwegian striker was particularly proud of the way City handled the pressure of playing away at Liverpool, where the contest remained goalless until Ryan Gravenberch was dismissed for a second bookable offence in the 62nd minute.
“It was tough and hard. We showed amazing character from Gigio at the back, all the way to the front. I'm so proud of everyone. It's always tough to come here,” Haaland said.
“It's about these times to stay strong mentally and stick together. And do what you can do something about. What we can do is play good football and fight together. That's the only thing we can do.”
City took advantage of their numerical superiority almost immediately. Haaland opened the scoring in the 65th minute, with Doku adding a second three minutes later before Cherki completed the victory in the 78th minute.
Haaland had missed a significant opportunity shortly before his goal but said he concentrated on remaining ready for another chance.
“I missed a big chance right before and it was just about focusing on getting another chance and stay focused. The moment came and I took it,” he said.
The striker also praised midfielder Elliot Anderson, who was named Player of the Match for his performance in the middle of the pitch.
“I spoke about the character at Old Trafford when we went down to 10 men and today again, the first guy I think of is Elliot,” Haaland said.
“Today again he controlled the game for us and he goes into the tackles. He does the things we need to do. He's a good player!”
City's win made it six victories from their opening six league matches. Haaland, however, was already looking ahead to the next challenge.
“There's plenty of games coming on. It's time to recover and already start focusing on the next one.”