The Reds defeated City 5-1 over two legs to reach the Champions League semi-finals in comfortable fashion.
Alexander-Arnold was one of Liverpool's best performers over the two matches, despite being given a difficult match-up in the form of City star Leroy Sane.
The 19-year-old feels he was singled out by City due to his relative inexperience, but believes he showed that strategy was unsuccessful.
"I guess Man City looked at it and [felt] I'm the weak link," Alexander-Arnold said following Tuesday's 2-1 win at the Etihad Stadium.
"Maybe that gave me that underdog mentality and [I] tried to prove them wrong. That's what I went out to try and do -- to go and prove them wrong and show them I'm not the weak link in the team.
"I think over the two legs I tried my best and did my best to win my personal battles and help us win the tie."
Sane has been one of the stars of City's phenomenal campaign, but Alexander-Arnold feels he more than held his own and helped neutralise the Germany international.
"You look forward to playing these types of games, these types of opponents and testing yourself when you can," Alexander-Arnold said.
"I got the opportunity to do that over the two legs and I tried to do the right things. Hopefully I came out on top and I hope everyone sees it that way as well."
Speaking on BT Sport following the game, former Liverpool star Steven Gerrard heaped praise upon Alexander-Arnold, and suggested he could be in England manager Gareth Southgate's World Cup plans, despite not yet being capped at senior level by the Three Lions.
"If you look at Trent's age, and the magnitude of the game over both legs, who he was up against, I think he has to be the star man over the two legs," Gerrard said.
"He's stood up so well, Gareth [Southgate] will know him well."