West Ham United boss Slaven Bilic says his side tried to be "too cute" against Sunderland but insisted they fully deserved the three points.
Both sides had hit the woodwork - Mark Noble saw a drive tipped onto the crossbar by Vito Mannone and Wahbi Khazri clipped the frame of West Ham's goal - before Michail Antonio struck after half an hour.
Sam Byram's pass down the right wing looked harmless until Patrick van Aanholt allowed Antonio to gather the ball and turn back inside.
The winger then strolled into the penalty area unchallenged before rifling his shot across Mannone into the far corner.
Sunderland laid siege to the Hammers' goal after the break, although home substitute Andy Carroll almost added a second when he volleyed against the bar.
"We deserved to win," reflected Bilic.
"We scored the goal, we hit the post twice and we could have had a penalty for a foul on Dimitri Payet.
"But more than a few times there were situations where we tried to be too cute.
"This is the Premier League. Until you score the second one there is always the danger you will concede.
"But did they deserve to win more than us? No way," added Bilic, who invited a West Ham United fan celebrating his 18th birthday to sit beside him at his post-match press conference.
Match-winner Antonio scored for the third consecutive home match, and boss Bilic paid tribute to the former Nottingham Forest forward.
"He's a good example for this new generation of players who are expecting first to get a chance and then they are going to show you how good they are.
"They don't need to deserve a chance.
"He probably dreamed about the Premier League for a few years at Forest or before in non-league football."
Goalscorer Antonio said: "They threw everything at us, it's a great three points and now we kick on to the next game.
"I put five-in-five of my finishes in at training [like the goal] so I thought I would have a go."
Antonio, who celebrated his goal by running around in a circle on the floor in a nod to Simpson's character Homer Simpson.
He explained: "I watched The Simpsons Movie the other day and I saw Homer do it, and I thought it looked hilarious so I’ll do it if I score.
"It was all planned, I told Nobes, I told Reece – I told all the boys and they said no way I’d do it, but I did! I think I pulled it off!"