And he also called on them to keep up their record-breaking winning streak when they head to Celta Vigo on Saturday.
Unai Emery's side came from a goal behind to beat Madrid 2-1 on Wednesday and record six consecutive league wins for the first time in their history.
But while Argentinian defender Fazio expressed his delight at his team's recent run of results, which has made them the most in-form team in the Primera Division, he is hungry for more points.
"We are on a very good run, we have a very positive dynamic and we have to keep it up," Fazio told the club's official website.
Sevilla have staged a remarkable turnaround in recent months, their recent string of wins a far cry from their dismal form at the start of the season, which saw them bottom of the table in September.
Fazio puts the team's initial struggles down to poor luck with injuries and so many new arrivals taking time to gel, but attributed the turnaround to the strength of their squad, with Emery able to rotate his team and still take all three points against Madrid and at Osasuna.
"We have a great group inside the dressing room, a readiness to train, and even the players that don't play regularly are there to support the team and chip in, and those that play, like against Madrid or in Pamplona, always do a good job," he explained.
"It's very important that everyone helps out, that's a big reason for this great run of wins."
Sevilla are fifth in the Primera Division, 17 points clear of Celta, who lie 12th in the table, but the Galicians are by no means safe, just four points away from the relegation zone.
Celta defender Inigo Lopez expects Sevilla to be in confident mood at Balaidos, but insists his team will not compromise their attacking philosophy on Saturday.
"They will come here with a boost after beating Real Madrid, but we will continue with our idea of going out to attack and wanting the ball," he told reporters.
"Sevilla are better than us in many aspects but they are not Real, Atletico Madrid or Barca. We have to fight for these three points."
However, Celta must improve on their poor home form, without a win in their last four games at Balaidos. And they are likely to be without talisman Rafinha, who is a doubt due to a toe injury which kept him out of the 3-0 defeat at Barcelona, plus centre-back Gustavo Cabral, who injured his ankle at the Nou Camp.
Sevilla meanwhile have no fresh injury concerns.