Ward was shown a straight red after just 20 minutes at the John Smith's Stadium having been adjudged to have handled the ball outside the area when challenging Junior Hoilett.
As things stand, the Liverpool loanee will miss the first leg of Huddersfield's playoff semi-final against Sheffield Wednesday as a result of the suspension, but Wagner hinted that he could challenge the decision.
"I haven't seen the video again but Danny says he touched the ball with his shoulder, not his arms or his hand. If we can clearly see the referee made the wrong decision, then we will appeal," he told reporters.
"What happened with Danny Ward is why it was good to bring in some fresh players for the Birmingham game. Joel Coleman played in goal against Birmingham and has had more minutes to work on his body shape and fitness.
"We were not switched onto the game and, even for me, it's not been easy to finish one competition and get ready for another. Now the competition that counts is in front of us. It's been a fantastic achievement but we will not go into the playoffs as favourites. We like the underdog role. Huddersfield Town are still in the race but we are humble as always."
The defeat means that Huddersfield finish fifth in the Championship table.