A 2-2 draw at the Stadium of Light left Wanderers still languishing inside the bottom three, but level on points with 17th-placed QPR, who play Chelsea at Stamford Bridge on Sunday.
He said: "I am very confident - I always have been because I know what we have as a group and I know how hard we are working behind the scenes to implement bits and pieces we want at our football club."
He added: "But within that, we realise that short-term, we have to make sure that we stay in the Barclays Premier League so then all the hard work we are putting in comes to a fruition.
"We will decide what happens to Bolton Wanderers. It's in our own hands to go and do that.
"We have taken 14 points from the last 24 - it probably should have been 16 on today's showing - so we know we are on a good run of form."
Sunderland boss Martin O'Neill was understandably disappointed after seeing victory snatched from his grasp, but admitted it was an illustration of the work which still needs to be done.
He said: "It would obviously have been great for us to win because at least for this evening, we would actually have gone into eighth position in the league.
"But I am not sure that we are an eighth-in-the-table team, that's the point. We are where we are.
"It was frustrating not to win the game today. I am disappointed, of course, but I said here a couple of weeks ago that we have work to do. That's not a problem."