It was a victory that sealed a third-placed finish for the Reds, and marked a positive end to an unexpected campaign for the 20-year-old, who played 19 times in all competitions.
But Klopp could have been without him for the season-closer at Anfield, having picked up a knock in the 3-0 win at Burnley in midweek.
“Even the good things this year, when they happened they didn’t feel too good very often, because 20 things around happened,” the manager said in his post-match press conference.
“The injuries was a subject that followed us through the whole year, it was really tough to take.
“Didn’t train three days, but could play today, so that was the lucky moment. But nobody knew that until a few hours before the game!”
Williams and Phillips were both in the wars on Sunday, with the pair sustaining head injuries and being forced to play on with cuts bandaged, which was symbolic of the Reds’ season at the back.
Earlier in the week, Klopp has promised to pay tribute to his defensive duo when the campaign was over, and he did so as he hailed them for reaching “an absolutely different level.”
“Today they both got a cut and everything looks like we’re 1-0 up but they go for them and those kinds of things,” he said, believing Palace had targeted his inexperienced centre-backs.
“So we had to fight through and the boys did that.
“Let’s talk about them. How they played is absolutely incredible.
“The steps they made this year, they should be very proud because it’s an absolutely different level now, I have to say. That’s really nice to be a part of that.”