The Blacks Cats had looked on course for safety a couple of weeks ago but two points from a possible 12 has seen the club dragged back into the scrap for survival.
Sunderland currently occupy 14th place in the Premier League table, three points above the bottom three.
Sbragia acknowledges that the games at the end of the season are often cagey and tense affairs, but he insists it is how his team react to this that will determine their fate this term.
"It's now that nervy time of the season," he told the club's official website.
"I regularly speak to other managers and most agree that the games now are very edgy and it's how you handle it, you have to accept the challenge.
"We have nine games left and every one is vital, we've got to be mentally strong."
Bad timingThe former Manchester United and Bolton coach takes his side to Manchester City on Sunday on the back of what Sbragia calls the worst performance since he took charge at the beginning of December.
"It was the worst we've played and to have that poor performance against Wigan was bad timing," he added.
"In my 14 (league) games in charge, we've only had one really poor performance. The disappointing thing is we thought the game was there for the taking but we just didn't perform.
"We can't make excuses about the pitch or anything else, it's down to us (the coaches) and the players."