Lens midfielder Cheick Doucoure joined the Eagles for £20million, Chris Richards arrived from Bayern Munich for £10m, while goalkeeper Sam Johnstone and winger Malcolm Ebiowei were picked up on free transfers from West Brom and Derby respectively.
However, Vieira has some injury woes ahead of the season opener against Arsenal on Friday evening with James McArthur, James Tomkins and Michael Olise unavailable to ongoing injuries, with Olise still 'a few weeks away.'
Vieira said: "It's important to keep stability to grow as a team and try to improve the squad, a couple of players came on and that will give us more challenges. We want players to make it difficult for me to choose the XI. We are short on numbers but I believe we can be more competitive than last year.
"The game tomorrow will be important for us to start as well as we can."
Vieira will hope to recreate the magic of Crystal Palace's 3-0 victory over his former side at Selhurst Park last season, and believes opening the campaign at home under the intimidating Friday night lights could give his youthful side an added spark come kick-off.
He said: "[Arsenal] are in a better place than last year. The new players have made them much stronger. They have the squad to challenge to be closer to the title.
"It is really important [to play at home] and it was really successful last year as our home record was really good.
"Playing the first game at home is an advantage and I'm really looking forward to the game. The fans are excited, we are really excited and we want to start the season well to give the fans a really good performance."
Vieira still believes it is critical for players to keep taking the knee after those in the Premier League decided to limit when they take the anti-racism stance this season.
Friday night's Premier League opener is one of the matches that will still feature the gesture, with other instances set to happen during the FA and Carabao Cup finals and specific No Room for Racism contests.
The Palace manager was adamant those were necessary in ensuring the message is still heard.
"It's good to keep taking the knee," he said. "I think there will be a few occasions that this initiative will be doing it.
"I think it's good because we can't stop it straight away, because there is a statement to make and I believe it is important to keep taking the knee.
"We all are about [ending] discrimination so this is the fight that we will take long, and that's why I believe we still have to take the knee."
Last season, Wilfried Zaha became the first Premier League player to stop taking a knee before matches.