The West Yorkshire outfit were level at the break after Joe Lolley made amends for his mistake with a stunning goal, cancelling out Mark Noble's opening effort, which came from Jonas Lössl's risky pass out to Lolley, who turned into trouble and was quickly dispossessed.
But the Hammers flew out of the blocks at the start of the second and led 4-1 by the 61st minute with Marko Arnautović scoring a sublime goal in which he flicked the ball beyond Tommy Smith and struck low through Lössl just 11 seconds after the interval.
That was followed up by Manuel Lanzini's brace, with Smith guilty of leaving the Argentine onside to find the bottom corner before the Terriers were caught on the counter for the fourth goal five minutes later, Lanzini firing in after Arnautović's good work.
"[It was] a disappointing, frustrating afternoon because of the situations and especially the moments before we conceded the goals. I think we were below par with too many individuals today," Wagner conceded in his post-match reaction to the media.
"First goal [was an] individual mistake from Joe Lolley, second one individual mistake after the knock down, third one we played the player onside who has to be clear offside. These are mistakes you cannot do in the Premier League if you like to get some points.
"Obviously what went wrong today is easy to analyse. We can be totally honest with ourselves that we made mistakes which you are not allowed to do to get points.
"Nothing what we like, [but] something what always can happen because my players are humans. To be totally honest we have had these moments two or three times in the season so far and if it's so obvious what went wrong it's easy to analyse.
"We know exactly what we have to do better and this is what we've done in the past, show the reaction, the character and bounce back. This is what we like to do."
Lolley the one at fault for West Ham's first goal in Wagner's eyes
Wagner felt that the first goal, in which West Ham robbed Lolley of the ball and released Noble to beat Lössl one-on-one was more down to error on the midfielder's part, rather than a mistake from the 'keeper.
"To be totally honest, the people who blame the goalkeeper have no idea how we play and haven't probably seen enough of us," he declared.
"This was a very easy situation for Joe to send back, or if he turns then he has to beat his opponent.
"Since two-and-a-half years we've done this in games and in training. He knows exactly what he has to do in the situation but he made a wrong decision, a mistake. It happens.
"It was good for him that he scored this great goal, for him and his confidence, because if you've done such a mistake then it's very, very good and important if you score a goal like he has done."
Wagner felt that the performance and result should not spark panic among supporters over their chances of surviving relegation and said it is simply a circumstance of the club's lowly resources.
"We know exactly, I've said it often, where we come from and we are totally humble," the German said. "A performance like today is part of our reality, like performances against [Manchester] United and Brighton are part of our reality. This can happen.
"It's nothing what we like but we have to be totally honest with ourselves that performances like today or individual mistakes like today, this can happen.
"This is why this player plays for us and we work with them and try everything to make sure that it doesn't happen more often or too often, but we are totally aware that it can happen.
"No-one else, than the players, are gutted about the mistakes they have done and we, like in the past, speak totally honest about what went wrong and then we will make it better.
"This was the case more often and I said this before, performances like this are as well part of our quality. Nothing what we like, but something what happens unfortunately."
Terriers boss not concerned by prospect of a basement battle
Huddersfield are now winless in their last five Premier League outings, their longest run without victory since promotion back to the top flight, with West Ham having moved above them and into 11th.
Asked whether it was a result that he worried would drag his side back into the relegation battle, Wagner replied: "No, absolutely not because for us I think - I'm not a stats freak like everybody knows - but we always in the season were more or less four, five, six points above the relegation zone so what happened? What changes? Nothing, apart from that we have one game less now.
"But we are more or less the whole season in and around this area apart from the points we were above, sometimes 11th, sometimes 15th in the table. But points-wise, the whole time we are more or less in this region.
"[This is] nothing what surprised us in a negative way because from day one, we were totally aware of what it's all about for us.
"For us, it's all about to survive, to fight for surviving and I think the players have done this absolutely fantastic so far, even if we were today below par. We will continue and try to do it better against Stoke.
And Wagner also hailed his side's ability to recover from setbacks and said: "This is for sure one of the biggest qualities this group of players has.
"First of all to be totally honest and analyse totally honestly, raise their hands and say: 'Yeah, this was not good enough' and then to work on it to make it better. This is what the group of players have done.
"They have great character and they have shown reactions always when it was necessary. For sure it is necessary to show a reaction after the performance today and the mistakes we've done."