Mauricio Pochettino's side were beaten 1-0 in the opening leg at Tottenham Hotspur Stadium, with Donny van de Beek's first-half strike enough for the Eredivisie side.
They were staring at a quarter-final exit against City, trailing 4-3 on aggregate with 17 minutes left of the second leg at the Etihad Stadium, only for Fernando Llorente's goal and Raheem Sterling's disallowed late effort to see them through.
And Lucas wants a repeat of those heroics in the Netherlands next week, saying: "The spirit against City was amazing, unbelievable. We need to play like that in Amsterdam.
"We went to the Etihad and played a very good game against City. We were strong mentally. Now we need to do the same: run, fight. I believe in my team-mates. Let's rest well now, prepare for the next game and believe always."
Lucas hopes Pochettino can work his magic after admitting the manager lost his temper at half-time of Tuesday's defeat.
"We gave them too much space and the coach said that in the changing room," said Lucas. "Was he angry? A little bit. He spoke to us, he did some changes. I cannot say everything because it's personal [private].
"You know Mauricio. He loves to touch our minds and to motivate. That's why we changed in the second half and played much, much better."
Moussa Sissoko also thinks it would be "foolish" to write off Spurs as they seek to reach the Champions League final for the first time.
"I believe we will go to Amsterdam and come back with qualification because I know the quality of this team," he said. "We have a lot of character. I think it would be foolish to write us off. We have proven that a lot of times this season.
"With 1-0, a lot of things can happen. Look at when we played Manchester City in the second game. In the first 20 minutes, there were five goals. Who would believe that? No one. So, hopefully, when we go to Amsterdam, we will score a lot of goals and get the qualification."