Matthews lashed the ball into the top corner from 20 yards after a powerful burst forward to edge Celtic into the William Hill Scottish Cup fifth round with a 1-0 win over Arbroath on Wednesday night.
The Wales international's only other senior goal came against Watford, but this was the first one he actually meant.
"I scored one but it was a lucky halfway line cross," the 20-year-old said. "I tried to put it in the box and it bounced over the keeper's head. I didn't mean it, so I can claim this one. It was much better."
Matthews, who joined Celtic 18 months ago, added: "I have waited a while. Luckily I caught it sweet and it went in the top corner.
"I couldn't have caught it any better and the direction of it meant the keeper had no chance.
"I have had a few shots on goal this season and been unlucky in a few games. Luckily for me that one went in and hopefully I can get a few more for the rest of the season."
Matthews set up two goals in Celtic's 3-1 win at Kilmarnock on Saturday, taking his Clydesdale Bank Premier League assists to seven for the season, and has revelled in the freedom offered by playing wing-back in Neil Lennon's 3-5-2 formation.
"I like to get forward and that formation allows me to do so," Matthews said.
"The last two games I have proved I can play both right-back and wing-back. Whatever formation we play I am happy to do so."