Born in Alaquàs, Valencian Community, Pallardó played a similar role to David Albelda as a holding midfielder.
In August 2008, already owned by the Madrid-based club, he was loaned to Segunda División side Levante UD for the 2008–09 campaign, thus returning to his native region.
[6] After a successful season a further loan was agreed,[7] and Pallardó was an even more important first-team member – 35 games, 2,662 minutes[8]– as the team returned to the top flight after a two-year absence.
[10] During his second spell at the Estadi Ciutat de València, he failed to make his breakthrough in the starting XI, also dealing with injury problems.
[15] Pallardó made his competitive debut for his new club on 4 October 2014, replacing Prince Buaben for the last 12 minutes of a 3–0 win at Queen of the South.