Joe Lolley went on to squander a glorious chance for the hosts at the death, meaning that they now have a replay to contend with in the West Midlands early next month.
Speaking to reporters after the match, a frustrated Wagner said: "It isn't the result which we wanted to have and I think it isn't the result we deserved.
"We missed out clear-cut chances, which we had a few of and we made two individual mistakes before we conceded the first goal as well. This means too many mistakes in the offence and too many mistakes in the defence and then it's difficult to win.
"We only have a draw, a rematch, nothing that we wanted to have, but now we have it, we accept it. I'm not too worried about the rematch because we have at the minute a very big, healthy squad."
Huddersfield, who made seven changes for Saturday afternoon's clash, will attempt to halt a six-game winless run in the Premier League when they face Liverpool in three days' time.