A positive Covid-19 test last week saw Vieira missing on the touchline for the second game in a row and the Eagles had several others unavailable including Wilfried Zaha and Conor Gallagher, but three first-half goals earned them more success at Selhurst Park.
Odsonne Edouard opened the scoring from the penalty spot after eight minutes before Jean-Philippe Mateta and Jeffrey Schlupp made the most of their starts to find the net during the opening 45, with a fourth victory of the campaign at home enough to move Palace up to ninth.
“We try to work in a way that makes sure we are not too reliant on one or two players to be match-winners for us, it is important everyone contributes, so I am delighted the other players stepped up,” Roberts said.
“The important thing when you score early is you build on that and don’t go flat. We managed to do that and it was an excellent first half and a really disciplined performance in the second half to see us through.”
Palace had lost 3-0 at Tottenham on Boxing Day and saw Zaha sent off to leave them further depleted for the visit of Norwich but Roberts and co were able to give Vieira something to smile about at home.
The club confirmed the positive coronavirus result for the former Arsenal captain on Boxing Day and with West Ham set to visit on Saturday, the Eagles could again be without their manager.
Roberts, despite a routine triumph over Norwich, is eager for Vieira to return.
“I don’t enjoy it at all because I want Patrick back in the technical area and back here,” the Welshman conceded when quizzed about filling in.
“My sole focus is on making sure everything he wants done, we do it to the best of our ability.
“Of course I miss him on a daily basis at work and we can’t wait to get him back with us because it is important for the staff and important for the players but for the meantime we will do everything we can to get through this period.
“He is doing well, obviously delighted with the result, and we are in constant dialogue.
“We’re just waiting day by day to see when he will be back at the training ground and back at the helm.”
Norwich boss Dean Smith saw Max Aarons, Todd Cantwell and Teemu Pukki added to his list of absentees the day before they suffered a fifth defeat in a row that leaves them bottom on 10 points after 19 matches.
“The result and scoreline hurts – I didn’t think it was a 3-0 but the manner of the goals we conceded were poor,” the Canaries boss admitted.
“It is tough at the moment. We are halfway there and we haven’t got anywhere near enough points as we would like.
“The optimism we had when we first came in has unfortunately ebbed away with the last three games and certainly the last three results, but we are lacking a lot of experience and leaders within the group at the moment who are unfortunately injured or ill.”