The club still sit six points adrift of safety, but Agnew has suggested that his team will only focus their attention on their next fixture - a home clash with Manchester City.
The 51-year-old is quoted by BBC Sport as saying: "It feels great. Everybody is absolutely delighted with the three points. We had to defend for long spells but we got the goal early. I'm so proud of the players.
"Clean sheets are obviously something you build on. I think it was important, the early goal. It gave everybody a lift and a confidence to see the game through.
"The players are all happy. I think all we do now is we remain focused for the game on Sunday against Manchester City. We'll certainly gain some confidence and belief going into games."
Boro's success over Sunderland was just their fifth triumph in the Premier League this season.