The victory in the Betfred Cup final over Motherwell means Celtic have won four consecutive domestic trophies under Brendan Rodgers.
They are currently top of the Premiership and begin their 2018 Scottish Cup campaign in January with a fourth-round tie against Brechin City.
“We always have the belief,” Roberts said. “The manager has the belief in us. We’ll keep plugging away and keep moving on with the games and that’s all we can do. At the end of the year we can look back again and hopefully do the same thing.”
Asked if the ‘double treble’ was possible, Roberts said: “Of course. I mean, you can see the quality in our side.”
Rangers came close to consecutive trebles in the 1990s. They won a clean sweep in 1992-93, then won the league and League Cup the following season but lost to Dundee United in the Scottish Cup final.