Leicester equalised four minutes later, with England forward Vardy converting a penalty after Chris Loew brought down midfielder Andy King at the John Smith's Stadium.
Craig Shakespeare's visitors came closest to picking up all three points but Vardy somehow managed to miss an open goal following a counter-attack led by winger Riyad Mahrez.
Huddersfield maintained their unbeaten run at home this season, with Wagner particularly impressed by his side's quick recovery from their loss to West Ham United on Monday.
"We got the response I wanted from the West Ham game in terms of the performance... the team showed great attitude," the German said.
"I was very pleased with the three players who made their first starts. We scored a great goal, but gave possession away too quickly afterwards and Leicester punished our mistake."
Shakespeare chose to look at the positives and praised Leicester for their fighting spirit after suffering three defeats in their first four league games.
"We have played better this season and got nothing, but that can happen. We were second best first half, but we showed character to get something. A point can here can still takes us forward," he said.
"We created chances second half and dug in while despite being a little off the pace."
(Reporting by Hardik Vyas in Bengaluru; Editing by Ken Ferris and Ed Osmond)
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