The Real Madrid star has helped Spain enjoy a golden period of international dominance, culminating in their 2010 World Cup success and European Championship wins in 2008 and 2012.
Despite that, Brazil and Argentina are the favourites to triumph in this year's edition of world football's showpiece.
Alonso – who has targeted a fast start in Spain's World Cup opener against the side they beat in the 2010 final, the Netherlands – feels his team have the experience to cope with the expectation.
Alonso told AS: "We have to know how to manage the pressure.
"We mustn't let it (pressure) choke us or get to us. I believe that the team has enough experience and knows how to play in these kinds of tournaments.
"Being Holland, a good side with young players who are eager to perform, we have to (be) very careful in this game.
"Because we know that if we don't win we will be in a very uncomfortable position."
Rounding off a tough Group B are Chile and Australia, with the latter given little chance of progressing to the last 16.
Australia dipped three places to 62nd in FIFA's latest rankings, announced on Thursday, meaning they are the lowest-ranked team to play in Brazil.
But Alonso rejected suggestions that Australia represent easy opposition and knows the danger of taking Ange Postecoglou's side for granted.
"We are expecting a difficult game," he added.
"These days there is less between sides in football and if you aren't at your best any team can make life difficult for you.
"As always, we will respect our rivals completely."
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