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."

Manager John Hughes had recently been quoted as saying the 46-year-old was likely to pursue another opportunity.
Latapy confirmed his departure in a statement on the Caley Thistle website without revealing his destination.
"I have never hidden my ambition to one day be my own man in management terms and believe now is the time," he said.
"My journey here has been fantastic and I have enjoyed every minute of my time in Inverness, culminating in us finishing third in the SPFL and winning the William Hill Scottish Cup, a massive achievement for any club let all alone ICTFC."
Latapy, who thanked Hughes for giving him the opportunity to be his assistant 18 months ago after a spell in a similar role with Boavista in Portugal.
The former Trinidad and Tobago midfielder had been Hughes assistant at Falkirk before a spell as his country's national head coach.
Caley Thistle chairman Kenny Cameron said: "Whilst we are particularly sorry to see Russell depart for pastures new, we fully appreciate his desire to further develop his undoubted talents in a new environment.
"Russell will always be remembered here at ICTFC, as a member of a great winning team."
Cameron hinted that Caley Thistle were prepared for such an eventuality.
"I recognise that any form of organisational change brings with it its own range of challenges," he added.
"I am, however, confident in our abilities to mitigate these challenges and look forward to working with the board and the club management as we seek to secure future successes for ICTFC."

The MP for Horsham in West Sussex said it was "time to make way for a younger candidate".
Mr Maude held ministerial positions in the cabinets of Margaret Thatcher and John Major as well as David Cameron.
He won his seat in the 2010 general election, defeating the Liberal Democrats, with a majority of 11,460.
In a letter to the Horsham Conservative Association, he said: "I was first elected to the House of Commons in 1983 just before I was 30, and will be nearly 67 by the time of the election in 2020.
"However, 27 years is a long time to serve as a member of parliament, and I believe now is the right time to make way for a younger candidate to carry the Conservative flag in Horsham."
Mr Maude was elected to the House of Commons in 1983 as MP for North Warwickshire, where he served until 1992.
After five years out of office he returned as MP for Horsham in 1997, which he has represented since.
Carlisle United manager Keith Curle has credited his club's "phenomenal" away support for their 2-1 win against Morecambe on Saturday.
[NEXT_CONCEPT]
Russell Latapy has left his post as assistant manager with Inverness Caledonian Thistle saying it is time to become a boss in his own right again.
[NEXT_CONCEPT]
Cabinet Office minister Francis Maude has announced he is to stand down at the next election, 32 years after entering parliament.