Replays showed that Stoke's winning goal on the night was offside, but Klopp believes that the luck eventually ended up in his side's favour during the spot kicks.
"It was great, the atmosphere was special. It was a good game for my side against a difficult side to play," Klopp told Sky Sports News.
"They changed their style today. It was [Jack] Butland to [Peter] Crouch so it was difficult to defend. We had a few problems, but they didn't have too many opportunities. Their goal was double offside but, in the end, we had luck in the penalty shootout. Over the whole 120 minutes, the players, crowd and Liverpool deserved it.
"Wembley is a cool place to play football... but we go there to win. It's not much fun to lose."
Liverpool will face either Merseyside rivals Everton or Manchester City in the final on February 28.