One of her Federation Cup doubles teammates was Mima Jaušovec, who Šašak teamed up with to win a gold medal at the 1979 Mediterranean Games.

She won a further gold medal four years in Casablanca at the 1983 Mediterranean Games, beating Laura Golarsa to win the women's singles.

Her best performance came at the 1983 French Open, where she made it to the second round, then took fifth seed Pam Shriver to a third set before being eliminated.

At the 1984 Summer Olympics in Los Angeles, Šašak represented Yugoslavia in the women's singles event, for what was then a demonstration sport.

This included Yugoslavia's run to the 1984 semi-finals, which they lost to eventual champions Czechoslovakia.