A total of 1,454 Carlisle fans travelled the 68 miles to Morecambe, making up 47% of the attendance.
"They were sucking the ball into the net - you could feel it," Curle told BBC Cumbria.
"It's phenomenal - the noise you can hear from behind the goal. You can tell there's a unity growing."
Carlisle came from behind and sealed victory with two goals in two minutes - a 83rd-minute Charlie Wyke penalty followed by a close-range finish from substitute Derek Asamoah.
"The pleasing thing is that at 1-0 down coming off the pitch at half-time, the supporters were with us," Curle, 52, continued.
"The supporters stayed with us because they knew there is a level of commitment within the players and within the staff that we want to do well for them and I think that shone through."
Carlisle sit 11th in League Two, three points below the play-off places, but with games in hand on many of the teams above them.
"I'm very proud to be manager of Carlisle United. I know there's a journey for this club to go on and I'm desperate to be a massive part of it," former Manchester City defender Curle added.
"I've said to the players - if we make the play-offs, we go up."
Carlisle United manager Keith Curle has credited his club's "phenomenal" away support for their 2-1 win against Morecambe on Saturday.