The win at the Liberty Stadium saw Brendan Rodgers' side leap above Welsh rivals Cardiff City to third in the Championship table.
"It was a couple of games overdue I felt but definitely glad to get off the mark," Moore said.
"The longer it goes on [without scoring], not so much for you, but people start talking.
"I was totally comfortable with the situation because I knew that goals would come... it keeps a few people quiet I guess.
Williams happy to flex goal muscle
Scott Sinclair's 19th goal of the season had given Swansea an early lead, the striker converting Angel Rangel's cross, before defender Ashley Williams doubled their advantage before half-time with a diving header.
Moore secured the victory from the edge of the area with 12 minutes left, firing home from the edge of the area.
"It's not easy playing number nine in this team sometimes because you don't really get chances but... when you play with such a good team you're always going to get goals," Moore added.
"The spirit within the squad is first class and I wouldn't accept anything less."
Swansea travel to Coventry City on Tuesday night before a clash with rival promotion-chasers Leeds United at the Liberty Stadium next Saturday.
Source: BBC Sport
Source: BBC Sport