Polášek was drafted by the Vancouver Canucks 21st overall in the 1992 NHL Entry Draft from HC Vitkovice of the Czech Extraliga with the hope of seeing the tall center develop into a player similar to Mark Messier. He however turned out being unable to live up to the expectations, failing to even make any kind of impact at the minor league level. During his stay with the Hamilton Canucks and the Syracuse Crunch, the then farm teams of the Vancouver Canucks in the American Hockey League, he registered only 20 goals over four seasons. Even further down, at the ECHL level, with the South Carolina Stingrays, Polášek was unable to perform at the level he was expected to, failing to even register a point in 7 games. In 1995, Polášek returned to his home Czech Republic with his former HC Vitkovice team. Even at home, Polášek was not the impact player the Canucks scouts once thought he should have been, scoring only 41 goals in eleven years in the Czech and Slovak leagues.
Those performances were unsurprisingly not well received by the Canucks fans. Usually regarded one of the worst NHL first-round draft picks the Canucks ever made - CNNSI.com’s 2001 profile of Canuck draft busts (Say it ain’t so: Transactions that broke our hearts) even states that “Polasek fared worse than the previous three (first-round busts Dan Woodley, Jason Herter and Alek Stojanov) combined -- he never played in an NHL game. In fact, one is hard-pressed to even find statistics on Polasek in many hockey annals.” The Vancouver Sun’s Iain MacIntyre also wrote in 2001 that if “nuclear winter” set in due to the Canuck draft record in the 80s, then the team “detonated the H-bomb on themselves in 1992 in the form of Libor Polasek, who soon vanished. Not so the Canucks' reputation for picking more duds than CBS programmers.”