The win ensured Barcelona became the first side in La Liga history to win all 19 of their home league matches in a single season. The achievement was made even more remarkable because the club played across three different stadiums during the campaign - Estadi Johan Cruyff, Estadi Olimpic Lluis Companys and Spotify Camp Nou.
Flick said the supporters had played a huge role in the team's success throughout the season.
"It has to do with the team and the connection with the fans," Flick said. "It's an amazing feeling because they give us 10 per cent more. The fans know when we need them."
The German coach also praised his players for their defensive effort against a dangerous Betis side.
"Today it was a bit difficult, but we wanted to win. It was incredible to see how we defended against a fantastic team like Betis."
The match also marked the final home appearance for veteran striker Robert Lewandowski as a Barcelona player, with the Polish forward receiving an emotional farewell from supporters after the final whistle.
Flick admitted replacing Lewandowski would be one of the club's biggest challenges moving forward.
"It was a perfect farewell," Flick said. "It was very emotional and you could see that he has Barca in his heart."
"I'm very grateful to Robert. He's a fantastic person and a world-class player. For the last 20 years he has been the best number nine in the world and it will not be easy to find his replacement."
Flick also explained why so many foreign players and coaches quickly develop a strong connection with Barcelona.
"Barca are the best club in the world and the people of Barcelona are incredible," he said. "Every day when I walk down the street, people are very friendly. You can feel it comes from the heart, and that's why people fall in love with Barcelona."
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