Villa missed last Sunday's La Liga game at Barcelona with a shoulder injury and was helpless as World Player of the Year Messi scored a hat-trick in Barcelona's 3-0 win.
"When the world's best player (Messi) has his day, it's difficult to stop him," said Villa, who has stayed with Valencia despite reported approaches from Real Madrid.
But the World Cup-bound player found the perfect answer on Thursday, scoring three times in an extraordinary 4-4 draw at Werder Bremen to clinch a place in the last eight on away goals.
NEWS:Valencia's Villa scores hat-trick in 4-4 draw
He also provided a timely reminder of the threat he poses with European champions Spain for whom his total of 36 goals in 55 appearances is bettered only by Raul.
"Here we are in the quarter-finals with a national product," Villa was quoted as saying on Marca's website.
"Eighty percent of the squad are Spanish. I am happy we can give some happiness not just to the Valencianos but to all of Spain."
Valencia began the last 16 tie as outsiders after being held 1-1 at home in the first leg but were 2-0 up in 15 minutes with goals by Villa - who scored with a powerful strike after being found free on the left of the area - and Juan Mata.
UNSTOPPABLE VILLA
Werder Bremen were far from finished and peppered the Valencia goal, mustering 27 shots on target, yet every time they seemed to be taking control, Villa struck again with aplomb.
Hugo Almeida pulled one back for the Germans midway through the first half and an equaliser seemed only a matter of time as Almeida and Aaron Hunt fired wide from good positions.
But on the stroke of halftime, Villa scored another goal, calmly placing the ball through a forest of legs into the corner after David Silva pulled the ball back from the byline.
Valencia, however, were quickly under pressure again after the break as Torsten Frings, with a penalty, and Marko Marin scored twice in five minutes to make it 3-3 with nearly half an hour still to play.
The Germans looked as if they were closing in for the kill but instead Valencia broke down the other end and Villa fired home another unstoppable shot to put them 4-3 ahead. Claudio Pizarro replied for Bremen but it was not enough.
"There are lots of ways you can read the game," added Villa. "We've scored four goals but also let in four. We've suffered and fought. This is an important morale boost for the team."
Delighted Valencia coach Unai Emery told the EFE news agency: "I don't think I've ever experienced such a crazy game. But we were the better team."
NEWS:Valencia's Villa scores hat-trick in 4-4 draw
