Wagner's side, promoted through the play-offs last season, have failed to score in 20 Premier League matches this term but still did enough to edge over the line.
Laurent Depoitre's goal gave the Terriers the lead at Stamford Bridge on Wednesday, Jonas Lossl making a wonder save late on after Marcos Alonso's bizarre equaliser.
And Wagner was full of praise for his players after Huddersfield guaranteed their Premier League place for another season.
"To be totally honest my English isn't good enough to describe what the players have done over the whole season," Wagner told Sky Sports . "Tonight I think we've seen everything that counts for us: desire, passion, attitude and togetherness.
"I believe that with patience, desire and spirit you can compete with top quality and we've seen today we at least tried it. We had some luck but this group of players deserve this unbelievable achievement.
"I never doubted them, it was about their mental strength. We have had some big dips, five defeats in a row, but we were always able to come back in the big moments.
"Of course we want to show everyone what we can do. In the Championship season we were predicted to be relegated and we got promoted so we are used to it.
"The Huddersfield Town fans, they are humble with their ambitions and have the spirit to work and fight, and that's what our team has too.
"I can't believe that we survived in this Premier League season, whatever happens happens but now we will celebrate tonight and tomorrow for sure."
Aaaaaaaand breathe— Mathias Zanka (@mzanka) May 9, 2018
Lossl's brilliant reaction save, tipping an Andreas Christensen header on to the post, ensured Huddersfield kept hold of the point they needed for survival.
"The feeling is overwhelming, it's what we fought for all season," Lossl told Sky Sports. "To finish here with these games against City and Chelsea is unbelievable. Mentally it was tough, really tough, they needed it, but we fought like nothing before.
"This was the most important save of my career, no doubt about it, I just needed to get my fingers to it. It's down to the whole team for the defensive work we did today, they didn't have a lot of chances.
"It's been up and down all season, we have a good coach who keeps a positive atmosphere in the dressing room. We had great performances individually but it's been all about the team."