Bradford were beaten finalists in last season's competition but two goals from James Vaughan ensured they would go no further this time round.
"We were brilliant. We grew into the game and the goal came at the right time for us because the crowd was starting to become a little impatient," Robins told Huddersfield's official website.
"We were a little bit sloppy in the final third, we need to be better going forward.
"Adam Clayton had a very good game for us and made us tick throughout, along with one or two others. Everyone put a shift in and tried to pass the ball."
In particular, Robins was keen to praise the clinical finishing of former Everton striker Vaughan.
"He finished his chances very well. His first was a powerful strike and I felt that it settled everyone down," added Robins.
"Considering we only worked on that shape yesterday, the lads worked very well together. It was a fluid formation and we moved the ball very well.
"The big test comes on Saturday (at home to QPR) and we can repeat the performance, I have belief that the players can do.
"We need to carry the belief that we showed into the next game and training sessions that we have.
"They showed tonight that they are very good when they pass and move the ball. They are all capable players."