Boro made the most of the few clear-cut chances they created to claim a 2-1 win, with striker Cristhian Stuani scoring two excellent goals.
Sunderland hit back in the second half, with Patrick van Aanholt’s close-range finish offering hope for the home side, but a dogged defensive display from Boro saw them hold on for Aitor Karanka’s first Premier League success.
When asked what he thought was the difference between the sides, Clayton said: “I think calmness in front of goal when we got the chance.
“It was a great strike from Cristhian for the first goal and Alvaro (Negredo) for the second one in the box as well, so we were clinical when we got the chance and we’ve seen it out in the end in the second half.
“We’ve got goals in the side, so we’ve always got a chance.”
Fellow midfielder Stewart Downing was fulsome in his praise of his team-mates, who now have a win and a draw since returning to the top flight.
He said: “It was always going to be difficult.
“We started very well in the first half, but second half I thought we made it hard for ourselves. We could have pushed on, but credit to Sunderland, they came back into it, but it’s a massive three points for us.
“The timing of the first goal was very important. Right throughout the team I thought we defended very well, especially in the second half. It’s three points, that’s massive for us and that’s four points now, so very good.
“Not many players in our team have played a lot of Premier League games, so it will give them confidence. It’s a team effort and that’s what it was.”
Sunderland manager David Moyes agreed with the Middlesbrough duo, pointing to the visitors’ cutting edge as the main reason for the Black Cats’ loss. He said: “I didn’t think we deserved to go in 2-0 down, I didn’t even think we deserved to go in 1-0 down, but that’s football.
“We didn’t take some chances we had and when they got theirs they took them. We were a bit unlucky we didn’t get an equaliser.”