Costa, who is La Liga's second top scorer with 13 goals and is on the books of Atletico Madrid, recently announced he would represent Spain and not his native Brazil.
Costa's decision has increased competition at the striker position in Vicente del Bosque's squad for next summer's World Cup.
"I am not upset that Diego Costa has chosen to play for Spain," Llorente said to Spanish sports newspaper AS. "Any player would want to play for the Spanish national team.
"Had I been in the same position as Costa, I would have chosen to represent the country of my birth but everyone is entitled to do whatever they want to do."
The 28-year-old Llorente, who is currently on international duty with Spain, is hoping to gain a spot in Del Bosque's squad next summer.
Llorente was a member of Spain's winning side at the 2010 World Cup and at Euro 2012.
"I am happy to have returned to the national team," Llorente said. "It hasn't been an easy year for me but my transfer to Juventus has been a good thing."
Llorente was used sparingly last season by Athletic Bilbao coach Marcelo Bielsa after declaring his intention to leave the Basque outfit.
He signed a four-year contract with Juventus this summer.