Romelu Lukaku netted at the start of each half, while Juan Mata controversially had a goal disallowed on the stroke of the break, which saw the Terriers exit at the fifth round for a second year running.
United won the game in two moments
Wagner thought his players were up to standard in a match, especially the first half, where Town really tested the 12-time FA Cup winners, saying: "Performance-wise, I think the players have done well.
"Performance-wise, brilliant without scoring goals and at the end that's what counts in football, this is why [Manchester] United deserved to win, they scored two goals and we haven't used our opportunities."
Lukaku made the Terriers' high line pay with his pace and power for both of his goals, and Wagner says United's high quality was the deciding factor in the end.
"We are smart and intelligent enough to separate our performance and result, especially if you play against an opponent like [Manchester United] with top quality, which they have shown in these two situations where they hurt us."
Terriers need to build on their momentum
Now Huddersfield turn their full attention to the fight for Premier League in their debut campaign as a top-flight club, a mammoth task, but something their head coach believes is achievable.
"We've now perform three times on a very high level, a very good level. Two times we won and one time we lost, we have the momentum which we always wanted to have and now we have to keep it for the final 11 games.
Momentum is key for any team battling Premier League relegation, but Wagner believes now believes his outfit have the momentum needed to push for safety.
"These are very important ones but we can look forward to it in a positive mood with the performances we've shown not only today, but in the last three games and this is what we work with."