Mata's club record move to Manchester United in January has failed to improve his international prospects while Torres has not done enough to impress either, with Manchester City's Alvaro Negredo Spain's most in-form centre-forward in the Premier League.
Manager Vincente del Bosque called up 23 players in total – the same amount he will be allowed at the World Cup in Brazil.
Despite the fixture coming just a few months before the World Cup, Del Bosque said it would be wrong to read too much into the players named or excluded.
“This is just a squad to play Italy, not for the World Cup,” he said. “Some players not on this list have a lot of merit."
Brazil-born Costa has represented the World Cup hosts in friendlies but revealed he wanted to play for Spain last year.
Del Bosque included Costa in his squad for two friendlies in November but he had to withdraw due to injury and the Italy match could mark his first appearance for his adopted country.
Even if he appears in a friendly for La Roja he will not be bound to Spain as only competitive fixtures count.
"Costa is there on merit for his form with Atletico Madrid. It doesn’t commit either party," said Del Bosque
Spain's latest squad, Del Bosque's last before he has to name a preliminary list in May of 30 players for the World Cup, has a distinctly Brazilian flavour as Bayern Munich playmaker Thiago Alcantara, the Italy-born son of former Brazil midfielder Mazinho, also returns after injury.
Midfielders: Xavi (Barcelona), Sergio Busquets (Barcelona), Xabi Alonso (Real Madrid), Koke (Atletico Madrid), Andres Iniesta (Barcelona), Santi Cazorla (Arsenal), Cesc Fabregas (Barcelona), Thiago Alcantara (Bayern Munich), David Silva (Manchester City)
Forwards: Alvaro Negredo (Manchester City), Jesus Navas (Manchester City), Pedro (Barcelona), Diego Costa (Atletico Madrid)