A key component of Jose Mourinho's Madrid team, Alonso has helped lead the battle with Barcelona for the Spanish and European trophies this season - and has been left with a feeling of what might have been.
"It's another stage of my professional career and I am enjoying it so far," he told liverpoolfc.tv. "We are challenging for big things and you want to be at a professional club. So far we are fighting against a great team like Barcelona, they are making it more difficult to win La Liga, for example, but that makes it a greater challenge than it already was.
"I want La Liga because that's the only trophy I don't have and is the one I am missing. I missed it in Liverpool and hopefully I will be able to make it in Madrid. The Champions League is obviously the Champions League, but I want La Liga.
"I am happy here. It's a big club, we have a great manager and a good team. It's been a very intense season. The cup final against Barcelona was really hard, the Champions League semi-final games against them were hard as well, but we kept fighting, but at the end we couldn't make it. Even just winning the cup, we are not absolutely pleased with the season but we feel we have progressed and are looking forward to next season."