The Eagles have enjoyed a fine debut campaign under the former Arsenal captain but back at the start of the season they were among the favourites to go down given it was a summer where veteran boss Roy Hodgson moved on and several experienced personnel left.
It has been far from a transitional period though with Vieira leading Palace to Wembley last month and they could set new club records in the Premier League with six points needed for a best points tally – while a ninth-placed finish would be their highest ever in the division.
“Being in the Premier League for the last 10 years I think is a good achievement but it is important for us to have this kind of ambition to do more,” the 45-year-old insisted with survival officially achieved after last weekend’s win over Watford.
“Now we are (established) in the Premier League, we need to grow our ambition and try to achieve more than just staying in the Premier League.”
Eleventh-placed Palace are one position and one point better off than Steven Gerrard’s men, who signed Philippe Coutinho permanently from Barcelona in midweek.
Vieira admitted that was a “massive statement” but wants his Eagles to win at Villa Park to remain on track for a top-half finish.
He added: “When you look at the talent that they have, obviously they’re not in the position where I believe they should be.
“It’s not just about finishing above them, it is about us finishing the season well and looking at ourselves and saying that we maximised the potential of the team and we are where we want it to be.
“So, it would be a really good achievement for the football club to finish in the top 10. With the summer that we went through and then after that it is about how can we grow from that? How can we improve ourselves? How can we try to bring those couple of players to improve the squad?”
The Premier League on Friday revealed Vieira was up for Manager of the Year while both Conor Gallagher and Tyrick Mitchell are contenders for the Young Player Of The Year.
Left-back Mitchell has not started the last three games but could return to the line-up after a minor injury on Sunday.
It has been a superb campaign for the 22-year-old but Vieira says the England international can be even better.
“There is a high belief and confidence in Tyrick’s talent,” the Palace boss said.
“He still of course needs to learn about the game and there are details in his game that he needs to learn to be better.
“Tyrick is about confidence and belief. I think there is still a big step for him to make about believing how good he can be and taking the initiative on the field.
“I think that he can bring more going forward to the team, because he has the quality to score goals, to make assists or to make more crosses. That will come with more belief and more games he plays in the Premier League.”
Vieira also confirmed on Friday academy graduates Tayo Adaramola and Jesurun Rak-Sakyi will get minutes before the season finishes.
“We have Jes and Tayo training with us,” he revealed. “They will be around the first-team for these three games and some of the games they will be on the field. We need to give and create opportunities for them to see how they will react under pressure.”
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