The late rally meant Barcelona became the first LaLiga team to win in the last 14 seasons when trailing by multiple goals entering the 80th minute, according to ESPN Stats and Information. In that span, teams facing a multi-goal deficit in the final 10 minutes of a match were 0-17-1,963.
"It was a spectacular comeback," Xavi said in a news conference after Barça, unbeaten through six LaLiga games this season, moved top of the league ahead of Real Madrid's game against Atletico Madrid on Sunday.
"We really believed until the end. We played with faith and courage. It was a comeback born from a will to win. When you don't play well, you need these qualities.
"We were taking more and more risks, leaving two at the back, everyone else on the pitch was an attacking player. We had to take risks and it came off.
"This shows the generational change we see in society. [The players] don't give up, 2-0 down, at home, but this generation fights until the end.
Celta had led through a first half strike from Jörgen Strand Larsen, with Anastasios Douvikas' effort 10 minutes from time silencing the home support and seemingly sealing an unexpected win for the visitors.
However, two Lewandowski goals, set up by João Félix and then Cancelo, paved the way for a brilliant Gavi cross to create a dramatic winner for Cancelo.
Xavi singled out midfielder Gavi, who replaced the injured Frenkie de Jong in the first half, for being at the centre of the turn-around.
"If we have to personify the comeback in someone, it would be Gavi," the coach added. "But this was a team effort. The [Celta] goal in the 80th minute was a hammer blow -- normally Barça don't come back from that."
Celta could have been out of sight in the second half but for the excellence of Barça goalkeeper Marc-André ter Stegen, who made several important saves.
"If the game had ended 4-2 to us, people would have said it was fair," Celta coach Rafa Benitez said in a news conference. "We leave with the feeling of 'not again' as has happened in other games this season when we have worked hard.
"I told the players at the end they should be angry and annoyed because we lacked purpose in the final minutes to stop the game a little and prevent the situations they created."
Xavi conceded that despite the euphoria of the win, the performance showed Barça still have plenty to improve.
"I agree with everything [Benitez] said," the Barça boss added. "We needed to compete better and show more purpose. We were not good at pressing after losing the ball. We could have lost and we will learn from that.
"The win tastes really good, but not better than [the 5-0 wins against Real] Betis and Antwerp, because that's our path. The path is those games, playing well, better ball circulation. When our intensity drops, the team suffers a lot."
Barça's success was also tainted by an ankle sprain suffered by De Jong, with sources telling ESPN that early estimates suggest he will be out for over one month.
"We need to see after tests on Sunday," Xavi said. "He is a strong player who doesn't come off lightly. If he's asked to come off, there's a reason for it. We hope it's not bad."