The Pilgrims bagged three vital points in a 3-1 victory - their first since December 3 - thanks to goals from Zak Goodson, Luke Shiels and Jordan Burrow.
But Simpson knows United must maintain their focus and use the victory to kick on.
“We have waited a long time for the win and we have to enjoy this feeling, but it's one game at a time,” he said.
“We have to back it up and we hope to build on it and take confidence from the win and see where it takes us.
“We understand the frustrations of the fans, but there's a long way to go and sometimes it only takes one moment to turn it around.
“The players needed a moment, a lift, and hopefully today is that.
“Everyone put a shift in. We've been on a tough run but we have got top players and players that care and want to be here.
“We will always be in a match with the quality of the forward players we have. Jordan Burrow was excellent today, it was a complete performance.”
Simpson also felt the win was a great reward for the hard work of boss Ian Culverhouse.
“The boss is an outstanding guy and it's a privilege to work with him and learn from him,” he said.
“He works his socks off day in and day out to take the club forward in every aspect. He deserves that win, but we have to back it up now, it's one game at a time.”
Goodson's 19th minute penalty set the Pilgrims rolling - with Shiels and Burrow striking in quick succession after the break to wrap up all three points.
Ben Liddle reduced the arrears with nine minutes to play - but the Pilgrims held on without too many scares.
United included goalkeeper Cameron Gregory for his debut, with Tom Nixon back in action too after sealing his midweek return from Hull City.
The Pilgrims edged in front when Goodson converted from 12 yards after Ben Pollock had been upended by Adriano Moke, presenting referee Callum Walchester with a straightforward decision.
United seized full control after the break. Billy Chadwick's 49th minute corner was met by Shiels, who saw his header blocked by Nathan Newall, before sweeping in the rebound while grounded.
Burrow added United's third goal three minutes later - tapping home at the back post after Tommy Taylor could only parry Nixon's cross from the right.
Shiels was withdrawn after an earlier collision and although Darlington pulled a goal back in the 81st minute through Liddle, following a Gregory save to deny ex-Pilgrim Kaine Felix, United held on.