The ex-Swansea City defender was handed the first Premier League start for the club in the game against Arsenal.
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."
“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.
5. Magpies bid for Guimaraes
Newcastle have submitted a formal bid of around £33.5m for Lyon midfielder Bruno Guimaraes. Arsenal and Juventus have also been linked. (Hugo Guillemet) (Photo by Buda Mendes/Getty Images)
Photo: Buda Mendes
6. Race on for Alli
Brighton are monitoring Dele Alli's situation ahead of a potential loan move from under Newcastle United's noses - with Burnley and Everton also interested in the Tottenham outcast. (Daily Mail) (Photo by Alex Davidson/Getty Images)
Photo: Alex Davidson
7. De Tomas in demand
Leeds United are reportedly interested in signing Espanyol and Spain striker Raul de Tomas, as are Arsenal and West Ham. (AS) (Photo by Alex Caparros/Getty Images)
Photo: Alex Caparros
8. Toon agree Rogerio terms
Newcastle United have agreed personal terms with Sassuolo left-back Rogerio over a move to Tyneside and are in talks with his club to sanction a deal. (Sport Italia) (Photo by Alessandro Sabattini/Getty Images)
Photo: Alessandro Sabattini