The Cumbrians were trailing 1-0 at Brunton Park when Symington was sent on for Jon-Paul McGovern midway through the second half and five minutes later the 19-year-old rifled a 30-yard free-kick into the top corner for his fifth goal of the season.
"As I was going onto the pitch the gaffer told me that I was on set-pieces and to make sure I hit the target if I was anywhere in range," Symington told the club's official website.
"I knew it was my first touch of the game. I looked at it and I thought to myself that I had a chance. Amazingly it went into the top corner.
"It's one of those where you know you've caught it sweet and you just hope it's going in."
Symington has made his first-team breakthrough this season after being handed his first professional deal in the summer and has been rewarded for some impressive displays with a new three-year contract.
"I looked round and saw everyone in the stadium going mad and I just wanted to take it all in," he added. "There isn't a feeling like it.
"The lads have watched me do it in training so they seem happy enough to step back and let me have a go. I'm on an absolute high now with the way that went for me."
- Sports & Recreation