Huddersfield were returning to the national stadium for the first time since they earned promotion to the Premier League in last season's play-off final, but there was to be no repeat of that day's joy as Son Heung-min scored in either half for Spurs.
“We’ve got beaten by a quality side," the German said. "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."
Son rounded Jonas Lossl after springing the offside trap to open the scoring in the 27th minute, before doubling his tally after the break by heading in from a world-class Harry Kane cross.
“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," said Wagner.
“It was not enough to cause Tottenham trouble, which we have to accept but we can leave Wembley with our heads up.”
Huddersfield had won their last two Premier League games before this one but their fate still hangs in the balance, as they sit only three points above the relegation zone.