Symington had only been on the pitch for three minutes when he delivered a thunderbolt, which earned Carlisle a share of the spoils in a closely-fought encounter at Brunton Park.
Former Carlisle striker Karl Hawley had given Scunthorpe a 52nd-minute lead, but Symington drew Carlisle level with a blistering 30-yard free-kick which gave Iron goalkeeper Sam Slocombe no chance as it tore into the roof of the net.
Abbott said: "Both sides deserved to take a point. In the first half you could tell we had had a week off, but in the second half we put them on the back foot a bit more. I thought our play deserved a reward, but I didn't think it would come like that.
"David is capable of that and he nearly got us a winner late on. It's the best goal I have ever seen.
"If it had been in the Premier League it would have been goal of the season. It was an unbelievable strike."
The Carlisle manager also had words of praise for recent signing Sean O'Hanlon. The arrival of the former Hibernian central defender has stiffened a shaky back four.
Abbott said: "I think we have found a real number five. He is tough, brave and honest."