The Blues finished fifth in the Premier League table, but ended the season with silverware after defeating Manchester United in the FA Cup final.
Azpilicueta believes that the Blues, who have now won 15 major trophies in as many seasons, are still able to pull in the world's best players.
"Of course big players will still want to come to Chelsea because we win lots of silverware," the Spaniard told reporters. "I have no doubt that the club will get a squad that can compete to win for trophies. I am sure that will happen.
"If the club decides that we need to get players in, I'm sure we will get the quality we want.
"It was important to win this season with a trophy. It shows we are still winners. When the results are not there, people look for something else."
Azpilicueta could play a part for Spain in the World Cup after being selected in Julen Lopetegui's squad.