Sunderland are now looking nervously over their shoulder at Hull, who are only a point behind, and at Newcastle, who are in the relegation zone and only two points behind.
All three sides face tough opposition on Sunday and Sbragia expects no quarter to be given.
"They are all hard games, no-one is going to lie down and put a weakened team out," he added.
"Hull have a got a very hard game against Manchester United and Newcastle have a very difficult game against Aston Villa.
"We don't know what Chelsea will bring into our game on Sunday - they might have one eye on their FA Cup final.
"But we know what we have got to do, it has always been in our hands and we know what is required on Sunday."
By contrast, Portsmouth caretaker manager Paul Hart has no such worries, with last Saturday's results ensuring his side's safety and the win against Sunderland coming with the pressure off.
Hart delighted to seal survival
Hart, who took charge at Fratton Park following the sacking of Tony Adams in February, said: "Saturday was an afternoon of relief. We have another year in the Premier League - and that is what I set out to achieve.
"I am delighted that the club is there and I think we deserve it. It is a smashing club and I really love it here.
"I am really pleased that we went about our job in a professional manner today, that we didn't take our foot off the pedal. We did justice to the Premier League.
"Obviously, it's been a very hard season and there are a lot of tired legs but they pushed themselves over the line."
Asked whether he would like the Pompey job on a permanent basis, Hart insisted he has not had a chance to even consider it.
"I was employed until the end of the season - specifically to keep us in the Premier League - and that is all I have been thinking about," he insisted.
"I was employed to do this job. It was specific - one day, one game, then it became until the end of the season and we have really just focused on that.
"I'm contracted to this club for two years anyway, so it's immaterial. It's a good job to have, it's a great club and I'm sure there'll be a lot of people fancying it."
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