Fabregas was an influential figure at the Ramon Sanchez Pizjuan, netting twice - his first goals for the club since February - as Tito Vilanova's side maintained their 100 per cent record in La Liga this term.
The former Arsenal captain told fcbarcelona.com: "We felt comfortable at all times. We dominated the match, but sometimes it can get complicated and we have to show our character - and that's what we did."
On recent criticism directed at him, he added: "I've always been at ease. I think there are a lot of people that needed to talk, opine and write stuff but nothing is wrong. I'm tranquil because I've gone through rough times before and I always manage to score again.
"Besides, it's much easier when you're playing with quality players like Xavi and Lionel Messi."
The visitors appeared to be heading for defeat when Piotr Trochowski and Alvaro Negredo fired the Andalusians into a deserved 2-0 lead, but Fabregas' brace pulled Barca level before substitute David Villa secured the win in stoppage time.
Sevilla were not helped by the 72nd-minute dismissal of Gary Medel following a clash with Fabregas, with Barca's final two goals coming while the hosts were attempting to hold on with 10 men.
"There's contact because he gets my face and, in the world of football, it's the intention that matters most," Fabregas said of the sending-off. "There's no reason to talk about it. In football these kind of plays are straight reds."
Barca's sixth win in as many games left them four points clear of Malaga at the summit, while Sevilla stayed fifth after their first defeat of the campaign.
Match-winner Villa, back on the scene after breaking his shinbone last December at the Club World Cup, was thrilled to have made the decisive contribution after being introduced as a 79th-minute replacement for Dani Alves.
"I'm happy that I was able to help the team in the little time I had," he said.
"Sevilla fought hard and they played well. Thank God that I was able to finish off a good collective play. We're taking the three points.
"A goal is always important, but only when it helps your team, like today. It's important to score when it means winning points, especially when you're playing against a difficult rival that leads throughout much of the game."
He added: "Everything can improve. You have to get better on a daily basis regardless if you win or lose.
"The team was courageous. We were losing 2-0 at the Sanchez Pizjuan. It's very hard to win here and it's even harder to mount a comeback, but Barca fought and that's why we won three vital points."