Yamal opened the scoring in the seventh minute after Barcelona capitalised on an error in Villa's build-up. Raphinha then struck twice after the interval, finding the net in the 52nd and 64th minutes to put the result beyond Unai Emery's team.
Flick was particularly pleased with the defensive performance, highlighting the collective work that allowed Barcelona to keep a clean sheet against a side he considered a strong opponent.
“The clean sheet. I'm really happy how we defended against a really good team,” the Barcelona coach told TNT Sports. “We were very compact and everyone was included. This is the most important thing.”
The home side's high press was also central to Yamal's opener, with Flick explaining that the goal came from the approach he wants his players to follow.
“This is our idea how we want to play football,” he said. “We try to press them very high, so that they make mistakes. We had this moment, were in the right position and we pressed them well, and they made this mistake and we used it.”
There was one concern for Flick, however, as Rodri was substituted at half-time after reporting muscular discomfort.
“We took him off at half-time because he felt some muscular pain,” Flick said. “It'll need to wait until Wednesday before we examine that and find out more.”
Emery felt Villa had opportunities to make the contest more competitive, particularly after Barcelona took the lead, but admitted his side had been punished for mistakes when attempting to play out from the back.
“We had clear chances to score, but we didn't take them,” the Villa manager told TNT Sports. “Today, Barcelona capitalised on a few of our errors when playing the ball out from the back – though that is part of our approach, to draw the opponent in.”
He also identified the physical challenge of facing Barcelona's high press, saying Villa had struggled to win individual battles against the home side's centre-backs.
“We need to be able to win more of those individual battles,” Emery said. “This match has provided us with a lot of valuable information that will help us improve as we compete at this level.”
The Villa boss remained convinced his side could learn from the experience, despite the scale of the defeat.
“The result isn't an image that we're happy with,” he said. “It's true that we're still building the team, and this experience should help us as we continue that process.”
Emery added that Villa's priority remained competing in the Champions League and securing their place in the competition, while recognising the need to improve against its leading sides.