In his second appearance for the club since arriving on loan from Schalke 04, the Turkish centre-half impressed as the Reds took control of the last-16 tie.
While Mohamed Salah and Sadio Mane scored first-leg goals in Budapest, Kabak was part of a sturdy backline that kept the Bundesliga side at bay to record a crucial clean sheet.
Speaking to Liverpoolfc.com after the game, the 20-year-old said: "It was so special for me because this was my first clean sheet and my first win in this jersey.
"I’m a new player, I’m a young player and there’s a lot of stars here.