Sevilla took the lead through Alberto Botia in the 42nd minute, but two goals in eight second-half minutes from David Villa and Lionel Messi turned the game on its head.
The win lifted Barca 15 points clear at the top of the Primera Division and also helped ease the pain of their midweek Champions League defeat to AC Milan.
And Mascherano says the Catalan club can be proud of their second-half performance.
"The best thing about the game was our capacity to react," the Argentinian said on fcbarcelona.com.
"Conceding goals is something we know we have to improve. They scored against us with their first attempt on goal.
"We were aware that we were behind despite playing well in the first half and that we had to turn the game around in the second."
Team-mate Dani Alves was also pleased with the way Barca turned things around, and is now hoping they can continue that momentum going into Tuesday's second leg of their Copa del Rey semi-final clash with bitter rivals Real Madrid.
The Brazilian said: "It was a strange match especially because of how cold it was, but in the end we managed to win.
"Sevilla forced us to work hard to win the three points.
"We have to improve in this regard but we can concede goals if we win. This is a game and we have to remember that other teams also play.
"It's an important week, and that's how we're approaching it. These are the types of matches that we like to play."