Vieira – a former Arsenal midfielder – celebrated his first win in charge of Palace with the familiar taste of success against Spurs.
Palace had played well without winning their first three games of the season and Vieira wants this to be the start.
“It is important for us to keep calm, keep working and try to improve,” the Frenchman said. “The group of players we have is ready to compete in the Premier League, it is just about how we can be consistent.
“We played well and scored goals, how can we play that well next week?
“It was a really good team performance, we started the game well with energy, we competed well. I am really pleased with the performance we had.
“What we want as a team is to win the game. We played some really good football but we couldn’t win games and we wanted that because it will give us confidence and that was the most important thing.”
It was a dream debut for Edouard, who joined Palace on transfer deadline day from Celtic.
He scored less than a minute after coming on as a late substitute and added a second in added time, getting his Palace career off to a great start.
Vieira added: “It is a dream start for him. He came on and there was more space and that allowed him to score those goals.
“For him to come on and score those two goals, it is really good for him. It will give him belief and more confidence to do well for the team. I am really happy for him because it will help the team in the future.”
Even before they were down to 10 men Spurs barely looked like scoring, with Harry Kane failing to touch the ball in the opposition penalty area for the first time in his career in games where he has played 90 minutes.
Their three previous wins were all by 1-0 margins and Nuno knows there is work to do.
“It is a big concern, we had enough quality and talent to play better,” he said. “We didn’t do it. Credit to Palace, they were aggressive and they didn’t allow too much time on the ball.
“We lost duels, many, many situations that I think we should do much better. In terms of offensive (play), much improvement is required.”
It was an afternoon to forget with Eric Dier’s early injury, the red card for Tanganga and the penalty where Ben Davies could not get his hand out of the way of Conor Gallagher’s cross.
“We had a lot of obstacles during the game to overcome. It was not easy for the boys today.
“But in the first half I think we were in control of the game, didn’t create too much but didn’t allow too much also.
“So both teams were in the game but the team losing a player and all these things…I think we overcame that and at half-time we spoke and the perspective was to improve in the second half – but it didn’t happen.
“Even in the beginning before the penalty, (when we were) one man down, we showed resilience, we were strong. and the penalty came.
“But a lot of situations we have to look at and be fair to say that we didn’t perform as well as we should.”