The teenage midfielder opened the scoring for Hibs with a 25-yard free-kick and Tom Taiwo soon added a second before Richard Brittain pulled one back with a second-half free-kick to set up a tense finale.
Hibs held on for the points and Butcher hailed Stanton, who scored for the second consecutive week.
"That goal just shows the confidence he has got and the ability he has got. It's a sweet left foot and he has a big future," he said.
"He has just got a real appetite for the game and wants to get on the ball, make passes and carry it forward. He asks questions of the opposition and has great, great energy.
"Sammy is a great football player and he excites you - he lifts you off your seat. It would have been justice if he had got another goal at the end, he deserved that."
Butcher was also impressed with the performance of Michael Nelson, who stood in as captain in the absence of the suspended Liam Craig.
"We have exciting young players but they are backed up by a resolute back five," he said.
"I must say Michael has been outstanding this week. We call him Admiral Nelson and he has skippered every team he has played at.
"But this was the first time at Hibs and he has shown great leadership this week by saying: 'We need to get back to basics'. I thought that is exactly what we did and we ground out the result."
County boss Derek Adams felt his side deserved at least a point after a strong second-half display.
"If we had made it 2-2, I think we go on to win the game because you can sense the nervous nature around Easter Road," he said.
"But we haven't been able to do that and I am disappointed to come away with nothing. We didn't deserve that.
"Particularly in the second half we were the better side, there's no doubt about that. We lost two soft goals to start with and Hibernian have not had to work for anything."