Nahki Wells gave Huddersfield a deserved lead at Pride Park before Derby cashed in on a goalkeeping error from Alex Smithies and the double dismissal of visiting defenders Joel Lynch and Peter Clarke to win 3-1.
"We've had a bad week, but here we saw a little bit more togetherness," said Robins.
"It's important we move forward as a group and take that into the next four games, as there's a lot of football still to be played.
"We've all got to stick together."
Huddersfield are without a win in their last nine league games and are six points above the relegation zone.
"None of us are happy with the outcome or with the run we are on," Robins added.
"If we show the application we showed in the first half, that will go a long way towards securing the points we need and the performances the supporters are looking for."
Huddersfield play Brighton (home) on Friday, then Yeovil (away) and promoted Leicester (home) before a trip to Watford on the final day.