Vieira was not in the dugout in north London after testing positive for coronavirus, one of a number of cases in the Palace camp which saw them try to get the Boxing Day game called off.
The Premier League refused their request and Spurs piled on the misery as goals from Harry Kane, Lucas Moura and Son Heung-min made it an easy afternoon for the hosts.
Palace, who saw Wilfried Zaha needlessly sent off in the first half, only made one change to their starting line-up but fielded a weakened bench with a number of players absent.
Roberts said that preparations were not overly affected, despite not meeting up at a team hotel on Christmas Day, but Vieira’s absence was felt.
The Welshman said: “It was late yesterday evening that the results came through. We were all tested.
“The good thing about the way we prepare is that we do that as a collective.
“There was no stone unturned. It would be true to say everything ran like normal, except Patrick not being there as our leader leading things on the day will always be something that we miss because we need him there.
“But we got on with it the best we could. We didn’t want to make any excuses and I thought we started well. The game turned after about half an hour.
“I don’t know how many we had with Covid, some returning from Covid, close contacts, injuries, but ultimately you saw that we were short of options on the bench today.
“We have been focusing football-wise throughout the week. Preparations have gone very well in a football sense.
“The last 24 hours we have been in our bubble just focusing on the game, leaving the other aspects to others at the club. We have tried to get on with it the best we can, but unfortunately we didn’t get what we wanted out of the match.
“We met at the hotel to prepare for the match, most times we would do that on the previous evening. It’s difficult to do that as a bubble these days with some uncertainty. As a coaching staff and players we do as we are told.
“We prepare the best we can and we managed to do that this morning as we would normally before coming to the stadium. We are professional, everybody has to adapt. It is something we had to live with and I am sure there will be other rollercoaster weeks.”
Spurs showed little mercy as they made it six Premier League games unbeaten under Antonio Conte to move within striking distance of the top four with games in hand.
There is a definite change in momentum at the club since the Italian arrived, similar to the affect he had at Chelsea, but Conte is keen to cool any comparisons.
“I think it’s different. I don’t like to compare different situations,” he said.
“Also because there’s too big a difference with my experience in the past. Also because I remember very well I started the season and when you start the season you have the possibility to work with your players and to also make decisions about your players.
“This is different. For sure we have to continue to improve, to exploit the confidence that is going to improve us. We know very well, I know very well, we have a big job to do.
“It’s good to get three points, to score three goals with your three strikers. It’s good to keep another clean sheet. We know very well we have to work very hard to improve the situation.”