The Spanish midfielder celebrated winning his 100th cap for his country by scoring both goals as La Roja eased to victory.
"We know Cristiano perfectly," Alonso told Telecinco after the game. "We are not surprised about his level because he has played that way during the entire year. The key is to play like we did today.
"We know that at this point every game is kill or be killed. We didn't have many chances but we played a good game and we are very satisfied."
Spain manager Vicente del Bosque defended his decision to start without a recognised striker against France, with Cesc Fabregas coming in for Fernando Torres.
"I trust [Cesc] Fabregas," he said. "We have three very good strikers, but I see him in good form to play.
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Jordi Alba was also pleased with La Roja's win and was especially proud of their first-half display against Laurent Blanc's men.
"I'm very happy with my performance, and with the team in general," he said. "The first half was very good but the second half was a bit more difficult.
"It will be a tough game against Portugal, like it was today but if we stick to our style we have a good chance to win."