Despite securing an opening-day away victory at Bolton, new Sunderland manager Steve Bruce was slightly disappointed his team did not win more emphatically.
The Black Cats took the lead after only five minutes when summer signing Darren Bent headed in a cross from Steed Malbranque.
The visitors produced many other chances in the opening stages, but could not add to their slender advantage.
Bruce believes that by the time Hungarian goalkeeper Marton Fulop made a crucial stoppage-time save, the result should have been beyond doubt.
"To be far we should have been out of sight by then," Bruce told Sky Sports.
"The first half: I can't ever remember coming and playing in a Premier League game with so many chances away from home.
"You always know that we need the second one but we couldn't get it but fair play to the goalkeeper in the end, he's produced a wonderful save which has obviously won us the match.
"But I think it would have been unjust if we had just taken a point from it."
Fulop also made a great save from Gary Cahill's header in the first half, but the former Wigan boss continued to insist that the contest should have been decided long before the Hungarian intervened.
"He's made two fantastic saves but I think that overshadowed our performance in the first half," Bruce added.
"We had four or five wonderful chances and the only thing that's niggled me today is not taking them because you don't get a lot like that and it was important that we killed the game off."
Bent, who made the switch from Tottenham for £10million over the summer, delighted a travelling contingent of 5,500 Sunderland fans with his winning goal.
As well as paying tribute to fellow debutants Lorik Cana and Lee Cattermole, Bruce complimented Bent on the immediate impact he made.
He said "All those weeks and phone calls that the chairman has made pay off when they do that. It was a top, top class header and I'm sure there's many more of them to come."