The Black Cats were dominated by Spurs in their 1-0 loss at White Hart Lane on Sunday but at least were able to make life difficult for Mauricio Pochettino's men.
The only goal of the game was scored by Harry Kane in the 59th minute following a defensive mistake from Papy Djilobodji.
"We had to hang on for a long time in the game," Moyes told Sky Sports after the match.
"I wanted us to play much better, but Tottenham's quality forced us to be the way we were. We found it tough against them, but we hung in, we made some chances ourselves, and maybe we were a bit unlucky.
"I think possibly the best chance of the game was for Steven Pienaar in the first half, and then we went down to ten men - it was tough at the end, but we still tried to make a chance or two.
"It was a tough game for us, Tottenham had most of the ball, we had to defend for long periods, but at least we gave ourselves a chance of winning it - we were never out of the game today."