Curle acknowledged that his side did not do themselves any favours by falling behind inside two minutes, but was proud of how his players responded to the early setbacks.
"Giving a Premier League side a two-goal start was not the ideal scenario, but credit to the players - they didn't melt or fold. And you have to say, Everton were fantastic," Curle told reporters.
"A lot of credit has to go to a lot of people behind the scenes who worked to get this fixture on. To have 17,000 people inside Brunton Park was phenomenal.
"I think it was only 57 or 58 days ago that the place was decimated because of the disaster of the flood, so to be hosting football - and hosting Everton - here was excellent."
Everton's reward for their victory is a fifth-round trip to face Bournemouth at the Vitality Stadium.