The Catalan outfit hit the woodwork four times, in addition to creating a number of clear chances, but a second-half strike from Joaquin Larrivey proved the difference between the two sides at the Camp Nou.
"We had a lot of mental strength to survive and the oxygen to score the goal. We must be fair and recognise that if Barca had scored first, things would have been very different, but we knew we could play," Berizzo told reporters.
"[Barca] had chances, but our goalkeeper did well. The success is not receiving comfortable. Beyond our defensive work, our means to an end were fine."
Celta have lost just once in the league this season and have been tipped to finish in the La Liga top four.