Having started their maiden Premier League campaign with back-to-back victories, Wagner made 10 changes to his starting XI and saw his side fall behind inside a minute to the League One outfit.
However, two goals in as many minutes at the start of the second period, the first a penalty from half-time substitute Philip Billing and the second from Joe Lolley, delivered a third successive victory for the Terriers in all competitions.
“We gave ourselves a mountain to climb after conceding a very early goal,” admitted David Wagner after the game.
“How the group reacted was excellent though - we scored two wonderful goals and were very focused after going a goal down.
“Unfortunately we didn't hit the target often enough and came under a bit of pressure in the last 15 minutes.
“But in the end a win is a win, we're still in the cup and we can be happy we are in the next round."
The German head coach was also delighted his fringe players were able to keep the winning momentum going after the back-to-back victories in the opening Premier League fixtures.
"Now everybody has these minutes and the feeling of success which is important to grow confidence," Wagner added.
"We have three consecutive wins and of course this helps to get more trust and belief in ourselves and helps us prepare for the big challenges in front of us.
"We are very happy with what we've done so far, three games, three good performances, three wins, we cannot ask for more.
“We've given every player 90 minutes so we are well prepared for what is in front of us and we have an important game on Saturday."
Town's boss also went on to praise goalscorer Lolley and youngster Jordan Williams for their performances against the Millers – confirming he wants to send the latter on loan for a taste of further match action.
"He's the fittest Joe Lolley I've ever worked with," Wagner declared. "He scored and hopefully he can progress and put everyone under pressure"
And on debutant Jordan Williams he added: “He has shown in pre-season and training that although he is only 17-years-old he is a good talent.
“Everybody knows at the minute we only have one right-back and it was a very good debut from him.
“Maybe a loan move could be good for him now because this is a great level for him.”