The Bournemouth loanee began the match on the bench at the Globe Arena and was introduced just shy of half-time due an injury to Alex Lawless.
The contest looked as if it would be goalless at the break but up stepped Butcher with a wonder strike – with his first touch no less – to set the Glovers on their way.
“I saw it pop up in the air and thought all I could do was try and get a good connection,” he told YTFC’s official YouTube channel.
“Luckily it dipped over the keeper and went in!
“I was just happy we scored and it went in! I thought the keeper was going to touch it so when it went in I didn’t know what to do, stopped and let everyone come to me.
He added: “Today’s game is so sharp and you’ve got to be ready and prepared just like you’re playing from the start.
“You’ve got to keep doing runs up and down the touchline to keep warm and sharp, keep an eye on the game because you can’t go into it thinking it’s going to be like any other game as each one is different.
“I did that and luckily it paid off.”
Morecambe got back into the match through Antony Evans’ close range effort on 53 minutes.
However, it proved a minor speed bump on Town’s way to three points as goals from centre-backs Alex Lacey and Bevis Mugabi helped Darren Way’s side their first victory since the end of January.
“We looked comfortable after the first goal,” Butcher said.
“It went 1-1 and it’s tricky from there. You see a lot of teams go the other way and go 2-1, 3-1 down, but we dug deep, created a lot of chances.
“We did a lot of work in the week on creating chances and getting shots on goal and that paid off.
“We’ve all stayed positive and we’re all working hard like it’s the first game of the season. We’re honest players down here. It’s good to get that win and hopefully we can build on it.”