Spurs warmed up for their Champions League tie with Juventus by easing to a 2-0 victory.
Spurs manager Mauricio Pochettino, who turned 46 on Friday, had asked his players to give him a performance and result worth celebrating and they convincingly delivered through two goals from Son Heung-min.
The defeat leaves Huddersfield three points above the bottom three on an afternoon when they lost both Collin Quaner and Alex Pritchard to injury.
But Wagner said: “We’ve got beaten by a quality side; we met quality, they showed quality but today we showed fighting spirit, effort, attitude and they were only too good for us.
“We have to accept that we tried everything that was possible. The second half was better than the first one and the players showed they wanted to get a better result than the one we got.
“I think the second goal showed everything; we had some good minutes before this goal, a half clear cut chance, but then we made a miss pass and an unbelievable ball from Harry Kane cost us.
“The second goal said everything about the game, a top-quality side against a side which has shown the attitude, effort and fighting spirit which you have to show when you’re a team like us, which fights to survive.
“It was not enough to cause Tottenham trouble, which we have to accept but we can leave Wembley with our heads up.”