And the 26-year-old marked the milestone with a clean sheet as the Clarets plugged the gap on next opponent's Watford to two points.
“We battled for every ball, battled for every header, defended well as a unit and we deserved that, it’s a big point," he said.
“You have to stay switched on, when you come up against a big club who enjoy a lot of the ball and I thought we did that really well today.
“Defensive wise we were solid, as a back five then the midfielders in front and the two up top, everyone stuck in, and it paid off for us in the end.
“We are at the bottom, there’s no hiding away from that. But the only way is up now, starting from today, fighting for every point and giving our all from now until the end of the season."
Roberts' last domestic start, prior to the stalemate against the Gunners, was close to eight months ago when the Swans missed out on a top flight return at the hands of Brentford.
The right back — who appeared from the bench as Burnley lost out to Newcastle United at St James's Park, which was the scene of his first ever outing in the top flight — had been on the receiving end of a 2-0 loss at Wembley Stadium, with team-mate Jay Fulton's dismissal making life even more difficult.
The summer signing made 64 appearances for club and country last term, featuring four times in the European Championships, and has since played in World Cup qualifiers against the Czech Republic, Estonia, Belarus and Belgium.
He said: “Any point in the Premier League is a big point, we have come here after not playing for a while, me especially, so it’s really pleasing for us all.
“I haven’t played for a long time; it’s been quite stop-start since I came here. But to get out there today and get a start was unbelievable for me.
“I hope I made the boys in there, the coaches, the fans and the club proud today."
Mikel Arteta's men finished the game with 76% possession and 21 shots on goal, forcing the Clarets to dig deep to claim a share of the spoils.
That might be good practice for when the likes of Manchester United and Liverpool arrive at Turf Moor in the coming weeks. “We’re not going to play teams off the park and we’re not going to be the better team every game we play, but we will do what Burnley do and fight until the very last game," Roberts concluded.