Having not won in the league since December, Wagner's side have fallen into the relegation zone.
And the German is hopeful Tuesday's win can translate into a positive result against Bournemouth on Sunday.
Wagner said: "We were not clinical enough in the opening 45 minutes. We could easily have doubled the score.
"I was very pleased with the performance, the effort and attitude. It was a fully deserved win against a difficult Championship side.
"We are delighted to be in the next round and to play Manchester United at home. First and foremost we are happy to have won as it is a win we required to build up the momentum for the Premier League."