Liverpool confirmed shortly before kick-off Clyne was not in the match day squad after suffering a rib/abdominal injury in the EFL Cup semi-final tie with Southampton on Wednesday night.
Klopp said before kick-off: "He [Clyne] can cope with many things and we hoped for the best but then he had this little issue at training yesterday and we had to wait.
"It was one of the final moments of the session. We spoke this morning and he thought there was no chance. So we made this change."
Instead, Klopp named Alexander-Arnold in his Premier League starting XI for the first-time. After a shaky start, the 18-year-old provided a solid performance at right-back, keeping Anthony Martial quiet before the France international was taken off after 65 minutes having failed to make a telling contribution to the match.
Klopp had considered moving James Milner over to right-back and naming Alberto Moreno on the left of his defence, but was pleased to see Alexander-Arnold repay the faith shown in him.
He told Liverpool's official website: "Nice, eh? It was clear in the beginning. Then you see [Anthony] Martial, one of the quickest players in the Premier League, in the first two situations it was difficult and he needed a little bit of time to adapt. But then he did brilliantly."
He continued: The decision was not that easy. The first impulse if Clyney can't play is Millie on the right and Alberto [Moreno] left – but I didn't want to change two positions because of one injury. I knew, with a new system, with a diamond which we played, to change both full-backs, I didn't feel too well [about]. We didn't have to be too brave to bring him, we thought he was ready for it and he proved it."