Having failed to register a single shot on target in their Boxing Day defeat to Fulham, Palace took control of this match with two first-half goals from set-pieces, both taken by Michael Olise and finished by Jordan Ayew and Eberechi Eze.
Palace have struggled for consistency in the first half of the season, but sit just outside the Premier League’s top 10 going into the new year.
“It was a really good team performance,” Vieira said. “I think we played really well. We were aggressive, we were disciplined and when we had possession we showed some quality. It was a really good performance.”
Asked if the win brought relief after the Boxing Day loss, Vieira added: “It was relief from people that had doubt on us, on the team, on the players, but I always say I know my players really well, I know how well they can play.
“It’s important for me and it’s important for everyone at the club to trust the players. We have to understand who we are as a football club. What is difficult is when you have a young group of players who are new in the Premier League, there will be ups and downs.
“I didn’t believe we were the worst team after the game against Fulham and I still don’t think we have the best team after today. I invite everyone to be a bit more consistent in their emotions and to control their emotions.”
Vieira credited goalkeeping coach Dean Kiely with the set-piece ideas that brought the goals.
“We are looking at all aspects of the game and set-pieces is of course one of them,” he said. “I think the ideas from Dino were good and the players executed it quite well.”
Bournemouth were playing in front of new owners Bill Foley and actor Michael B. Jordan, who will have a clearer idea of how much work is in front of them as they sit three points above the drop zone.
Gary O’Neil, who had been struggling with a virus coming into the game, saw nothing to raise his spirits in a performance he said ranked “bottom” since he took over.
“I think it’s the first time since I’ve taken charge that we’ve fallen well below the standards that we’ve set,” he said. “I’m very disappointed with nearly all aspects of today.”
Illness and injury within the squad have not helped, but O’Neil said there could be no excuse for such a poor display
“I’m furious about the goals,” he said. “If we defend the set-plays like we’ve worked on neither goal occurs. Defending set-plays has been a thing all season we’ve struggled with but they were avoidable today.
“We miss (Marcus) Tavernier, he’s been fantastic for us and had an incredible impact…of course we miss him. But I hate excuses. I’m not looking for excuses. I take full responsibility. It cannot look like that in the Premier League because it’s ruthless.”