The Reds' defence of their Premier League title unravelled early in the Dutchman's second season, and they finished a distant fifth, 25 points behind champions Arsenal.
Many of the squad, including Kerkez, were already preparing for the World Cup when word reached them on May 30 that Slot had been dismissed after two years in charge.
"I was surprised," said Hungary left-back Kerkez. "I really didn't know. I was back in Serbia, I was sleeping and my brother woke me up. He knocks on my door and it was a big surprise.
"Nobody knew. I couldn't believe it, I was like: 'wow!' I have been in touch with him since, we have exchanged a few messages. That's it."
Kerkez joined Liverpool last summer from Bournemouth for £40m and made the left-back spot his own, playing 34 league games and limiting the game time available to Andy Robertson, who has since left the club to sign for Tottenham on a free transfer.
The move reunited Kerkez with Andoni Iraola further down the line, with the Spaniard having been appointed as Slot's successor and having previously worked with the left-back during two formative seasons together at Bournemouth, a spell in which Kerkez developed into one of the Premier League's most exciting attacking full-backs and earned a place in the PFA Team of the Season.
Speaking separately about Iraola's appointment, Kerkez did not hide his delight: "I was delighted, honestly. I worked for him before, and he helped me and improved me a lot in the two years that I spent with him. I was really happy, obviously for myself but also for the team."
But Kerkez says the standards shown by the squad last season will not be acceptable again under the new regime.
"Obviously [last season] was tough for everyone," Kerkez says. "When you are here, you need to play to win things. We had tough moments. We had moments when we fought back and then we had tough moments again. It was a good experience.
"You can learn a lot, pick up a lot. It wasn't good for our standards but we need to improve this year."
With pre-season now under way, including a friendly win over Sunderland in the United States, Kerkez is aiming to use his familiarity with Iraola's methods to help drive the squad's response to a campaign that fell well short of expectations.