Filip Sasínek first appeared in 2011 in the 800-meter run in national competitions. A year later he became Czech U18 champions over 800 meters both indoors and outdoors and also competed in U23 and adult competitions, where he was also able to achieve top positions. In 2013 he took part in international championships, the U18 World Championships in Donetsk, for the first time. There he first started over the 1500 meters, in which he did not get beyond the lead. One day later he made it into the final over the 2000 meter obstacle, which he finished in eighth place in the final in 5: 47.90 minutes.
A year later, Sasínek also competed in the U20 World Championships on these routes , with the obstacle course going over 3000 meters due to the higher age group. He finished the races in 25th and 14th place respectively. In 2015 he started for the first time in international championships for adults. The European Indoor Championships took place in Prague in spring . There Sasínek competed over the 800 meters and took 32nd place overall. Also at the U20 European Championships 2015 in Eskilstuna, he did not get past the lead in the obstacle course. From the 2016 season, Sasínek then focused more and more on the 1500 meters. This is the route he used to compete in the European Championships in Amsterdam. There he made it into the final, in which he finished eighth in 3: 47.76 minutes.
In spring 2017, he celebrated his greatest sporting success to date, after winning the bronze medal at the European Indoor Championships in Belgrade over 1500 meters. In the summer he started at the U23 European Championships in Bydgoszcz, where he won the silver medal in 3: 49.23 minutes. After only being able to compete sporadically in 2018, he finished fourth at the European Indoor Championships in Glasgow in 2019 . In October he started at the World Championships in Doha, where he was eliminated from the preliminary run in ninth place and finished in 27th place. In 2020 he won for the second time after 2017 at the Czech Championships in Pilsen over 1500 meters and set a new championship record in 3: 36.72 minutes.