Sbragia took over at Sunderland in November last year following the departure of Roy Keane, with Sunderland in serious danger of being relegated.
After an initial upturn in fortunes the former Manchester United reserve coach was unable to prevent another slide down the table, resulting in the nervous final day's action.
'I've had a chat with Niall [chairman, Quinn] this week and I think we need a bigger name to carry the club further. I've done everything I needed to,' said Sbragia
'I was given the opportunity to manage the club – and I've kept them in the Premier League. I would like to have done it better but I'm really pleased we stayed up.'
"I've loved it. There's been a lot of pressure - we started so well and maybe got carried away, losing our focus - but I always thought we were good enough to stay in the Premier League.
"I would like to have finished it today with a win but I'm pleased for the players and my staff. We've got a foundation and I'll be thoroughly enjoying seeing Sunderland move up that table.
"I'll come back in the next couple of days and tidy things up but I'll enjoy tonight and I'll look forward to some time on my own reflecting on what's happened in the last five months."