Leverkusen had kept their unbeaten run going with some incredible last-minute heroics but that was never an option against an Atalanta side who were in control from the outset.
Ademola Lookman scored a hat-trick to secure a first trophy for the Italian club in 61 years and end Leverkusen’s hopes of completing the season unbeaten, as well as winning a treble of trophies.
“We weren’t able to play as we wished,” added Alonso.
“After the first goal they showed a great deal of energy and we couldn’t find solutions to counteract that.
“We couldn’t impose ourselves or fashion goalscoring opportunities.”
Leverkusen need to swiftly switch focus to ensure they finish a memorable campaign with a second trophy.
On Saturday they face second-tier side Kaiserslautern in the German Cup final as they look to complete a domestic double.
“To achieve what we have for a club like Leverkusen is great,” Alonso added on TNT Sports.
“To be in the last week of the season having lifted the Bundesliga and playing [the Europa League final], we couldn’t make it, but then going for the Pokal [German Cup] too means a lot.”