Picak was promoted to Dinamo Zagreb's first team in the summer of 2009, becoming the third-choice goalkeeper behind Tomislav Butina and Filip Lončarić after the club's previous second-choice goalkeeper, Ivan Kelava, was loaned to Lokomotiva Zagreb.
He made his competitive debut for the first team on 6 December 2009 in Dinamo's 4–1 away win at NK Međimurje in the Croatian First League, playing the whole match due to injuries to both Butina and Lončarić.
In January 2010, Picak was sent to Lokomotiva Zagreb with whom he initially signed a stipend contract.
He did not appear in any competitive matches for the club until the end of the 2009–10 season, playing for the U19 team and serving as back-up for fellow Dinamo Zagreb loanee Ivan Kelava, and the club signed a 7-year professional contract with him in August 2010.
Up to date, he won a total of 33 international caps for the Croatian national football teams at the under-15 to under-19 levels.