Luton scored with a Elijah Adebayo header on the stroke of halftime, but City fought back with two goals three minutes apart from Bernardo Silva and Jack Grealish to return to four points behind Premier League leaders Liverpool.
"They don't need to prove to me what they are capable of," Guardiola said in a post-match news conference. "This is an extraordinary group of players and characters. But the competition and demand is to prove it again.
"In general, it is normal. 'Yeah City is not the same, City is over.' That's nice. Let them prove them wrong. We want to compete, I want to be there. It's so nice. I said before, we need that."
The result meant City snapped a four-game winless streak that threatened to derail their season as the reigning treble winners chase an unprecedented fourth consecutive Premier League title.
An upset seemed possible at halftime when City found themselves a goal down despite a dominant, if unthreatening, first-half performance, and Guardiola revealed how he motivated his side in the dressing room.
"I said to them, 'What do we have to do? Feel sorry for ourselves? We don't have to feel sorry for ourselves. It's football. This happens," Guardiola said.
"Now what do we have to do? Play the game? Complain to ourselves? Strikers, be more aggressive, score goals. Let's better defend the cross in the last minute and be positive. We have to demand more from ourselves.
"Big characters and big teams -- like this team is -- that defines a team. When we won games 4-0, win 15, 16, 17, 18 games in a row, that doesn't define who we really are."