Mallorca lost to Athletic Bilbao on penalties.
Rodriguez scored in normal time and said: "First of all, congratulations to Athletic and all its people. I get excited because I am very proud of my colleagues and the people.
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"It was a dream that we could lift the cup but it was not to be. We knew they were going to demand a lot from us. The effort has been impressive and we should be proud of what we have achieved.
"We have tried but there has been no way."