James Rodriguez's 81st-minute opener was cancelled out by Raul Garcia's goal as Atletico took the upper hand heading into Friday's second leg.
Alonso wondered what could have been but said the tie was still open for both teams despite the draw at Santiago Bernabeu.
"They [Atletico] demanded a lot of us and are very compact. It's a strategy they're good at," he was quoted as saying by AS afterwards.
"They drew level and it could have been a better result for us but it's still open for the return."
Toni Kroos enjoyed a strong game for Real and Alonso talked up the Germany international afterwards.
Kroos almost scored in the second half, volleying over the bar, before playing a part in Rodriguez's scrappy goal.
"It's easy to play with big players like him," Alonso said of Kroos.
"Despite his youth he has experience at the highest level and is a great signing for the club."
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