Born in Sa Pobla, Majorca, Balearic Islands, Crespí finished his development at local RCD Mallorca.
He made his senior debut whilst on loan, successively representing Segunda División clubs Granada 74 CF,[1] Xerez CD[2] and Elche CF;[3] he scored his first goal as a professional on 9 March 2008 while at the service of Granada, in a 2–1 away loss against CD Castellón.
[4] After returning to the Estadi de Son Moix, Crespí's maiden appearance in La Liga took place on 3 October 2010 when he played the entire 1–1 away draw with FC Barcelona.
[7] In the following transfer window, he returned to his country and joined second-tier team Racing de Santander.
[8] In the summer of 2013, after being relegated, Crespí signed a one-year contract at fellow league side CE Sabadell FC.