Bayer Leverkusen's German league and Cup double was the result of players keeping faith in the team throughout what turned into a dream season, their coach Xabi Alonso said on Saturday.

Leverkusen added the German Cup to their Bundesliga crown with a 1-0 victory over second division Kaiserslautern.

"In the end, to win like that meant we showed spirit, we fought for the fans for the club," said Alonso. "It is huge success to win the double. We will remember this in the future."

Leverkusen lost only one of 53 matches across all competitions this season, their only defeat coming in Wednesday's Europa League final against Atalanta.

They bounced back on Saturday, however, and despite playing with 10 men for more than half the game they snatched the win courtesy of Granit Xhaka's 16th-minute goal.

"The most important thing was the belief of the team. They were ready to battle with 10 players and I am proud of that," Alonso said.

"I need time to accept what happened this season. It was a dream season and to celebrate the last day like this here is special."