The German boss said the win offered fresh belief and confirmed his side were on the right track.
In a pulsating encounter at Balaidos, Lewandowski marked his return to the starting-XI with a hat-trick (10' pen, 37', 73'), while teen sensation Lamine Yamal added a fourth for Barcelona just before halftime. Celta fought back twice through Sergio Carreira (11') and Borja Iglesias (43') to keep the home side in the game, yet Barcelona's dominance in the second half proved decisive.
Flick emphasised that although the first half still contained mistakes, his team's second-half display offered a platform for confidence moving forward. "We played a good game with the ball and in the second half we defended better, the second half gives us confidence for the upcoming matches," he said.
He also brushed off external criticism of his tactics, remarking: "There's too much noise around us. We've improved and we're on the right track."
On Lewandowski's contribution, Flick added: "It's too early to decide. After the injury, I've seen a different, more positive Lewandowski; he's returned ahead of schedule. It's great that he's scored three goals, which shows his confidence."
Meanwhile the sending-off of Frenkie de Jong for two yellow cards late on will see Barcelona miss one of their key midfield operators in the next league fixture versus Athletic Club. Flick stated: "He had a great game, he controlled the match. He's very important for us, It's not good that he'll miss the next game; we'll have to manage it."
Heading into the international break, Flick noted the importance of maintaining momentum: "It's always better to go into a break with a win. I hope everyone comes back healthy from the break."
With Barcelona now just three points behind Real Madrid after 12 matches, Flick reaffirmed that his team will focus on their own progress rather than their rivals: "We're only focused on ourselves."
It was a night where tactical discipline, resurgence and star performances aligned for Barcelona, and one where Flick's clarity of message seemed as significant as the three points earned.
Pep Guardiola celebrated his 1000th match as a manager in fitting fashion on Sunday, guiding Manchester City to a commanding 3-0 win over Liverpool at a rain-soaked Etihad Stadium.
La Liga served up a gripping weekend of twists on Sunday, as Robert Lewandowski's hat-trick inspired Barcelona to a 4-2 victory over Celta Vigo, cutting Real Madrid's lead at the top to just three points after their stalemate at Rayo Vallecano.
Real Madrid are closely tracking the progress of academy graduate Jacobo Ramon, whose impressive form in Serie A with Como has caught the attention of head coach Xabi Alonso.
Xabi Alonso is facing a tactical dilemma at Real Madrid as the club debates how best to shape the future of Turkish prodigy Arda Guler.
