Dutch winger Arjen Robben was the latest high-profile player to suffer an injury ahead of the tournament in South Africa starting on June 11 and other casualties include the captains of England and Germany, Michael Ballack and Rio Ferdinand.
"The aim of our training camp, apart from finding our rhythm and learning ideas and tactics, is not to get injured," Mata said at a news conference at the European champions' base outside Madrid.
"There are important players who are not going to be at the World Cup and let's hope it doesn't happen to us and we all are able to travel at full fitness."
Left back Capdevila added: "The truth is yes, it's worrying. We are being careful because the aim is to arrive at the World Cup in peak condition."
Coach Vicente del Bosque had a scare during training on Sunday when Gerard Pique pulled up after a knock on his left knee but the Barcelona central defender was able to continue after brief treatment from medical staff.
A goal from striker Fernando Torres, apparently back at full fitness after knee surgery, drew the biggest cheer of the day from the hundreds of watching fans.
Capdevila said England's injury problems would hurt their chances in South Africa but that they nonetheless remained one of the favourites to lift the trophy on July 11.
"The great players want to be there and help their national team but if they can't participate they'll be giving their support to their team mates," he said.
"The injuries are significant but you don't lose a World Cup due to one player being sidelined," he added. "They (England) still have a good chance."
