A below-par start to their domestic season with only one win in seven La Liga games has put them 13th in the 20-team league and they have yet to score a point in their European Group A campaign.
"Sometimes when you come to difficult opponent like Manchester City... it brings out the best football in you," Garrido told a news conference.
"What's really important for us is to show a much better face of Villarreal than we've showed so far this season.
"We were recognised just a few months ago for our excellent football, our confidence on the ball, what we need to do now is try to rediscover that inspiration and prove again what we worked so hard for in qualifying for Europe last year."
While City's Champions League showings have been little better, with the English side picking up one point in two games, their domestic form has been rampant as they have surged two points clear at the top of the Premier League.
Garrido pointed to Saturday's 0-0 draw at Getafe as signs Villarreal were turning a corner but said nothing other than a win would do at the Etihad stadium on Tuesday.
"I want to see my team taking the initiative, showing our class, showing our quality on the ball, trying to get more possession," said the coach, who is treating this game and the return next month as "knockout" games.
"It means jumping higher, running faster and tackling harder - everything really that goes towards a good performance."
Coming up against a City team who have scored 27 goals in eight league games, Villarreal goalkeeper Diego Lopez was expecting a busy night.
"Yes, I suppose we are mindful of the fact we are playing against the leaders of the English league," he said.
"We've got to show we're up to it. Although we treat our opponents with respect, it is important that we come here with desire and a determination to give a good account of ourselves tomorrow night."
Bayern lead the group with six points from two games, with second-placed Napoli on four. City are third with a point, while Villarreal are bottom.
