Spurs' quality too much for Terriers
The South Korean opened the scoring on 27 minutes and Wagner puts his side's failure to get back into the game down to the quality of opposition.
Speaking to Sky Sports after full-time, he said: "We got beaten by quality. There's no doubt they were the better team and it was a deserved defeat, even though in the second half we tried what we were able to do.
"But we got beaten by quality, that's something we have to accept."
Despite the defeat, he was confident that Huddersfield would be leaving Wembley with their heads held high and is already focusing on a major clash next weekend.
"We have said this before, I think everybody is able to leave with their heads up and we will prepare for a very exciting game which we have next at our fortress of the John Smith's Stadium [against Swansea City next Saturday]."
Swansea and Palace up next
The West Yorkshire club's next two fixtures pit them against relegation rivals Swansea and Crystal Palace in what could be season-defining outings.
Both are at home though, and Wagner explained that the feeling is excitement, stating: "So excited to have two home games. This is where it counts and what we have shown in the past at home and the support we have had."
The atmosphere at the John Smith's Stadium has been terrific all season long, and the manager has called on the fans to once again spur the team on in both games.
"For sure Saturday will be the best support we have ever had, because everybody is fighting to survive, the supporters as well, and we will prepare as well as we can."