Born in Rijeka, Šarić started his professional career at local club NK Rijeka back in 1989. He went on to move to Spanish club Sporting de Gijón in 1993 and subsequently returned to Croatia signing with Dinamo Zagreb in 1995. After five years with Dinamo, he moved abroad once again signing with Greek club Panathinaikos for the 2001 season. He stayed at Panathinaikos until the summer of 2003 and then returned to his home town by signing a four-year contract with NK Rijeka.
Šarić was also an almost regular member of the Croatian national team between 1997 and 2002. He won a total of 30 international caps, but failed to score any goals. His only major tournament was the 2002 FIFA World Cup, where he appeared in all of the Croatian team's three group matches and was a starting player in two of them.