Alonso picked up a yellow card in Real's 4-0 second-leg semifinal win over Bayern Munich, ruling him out of Saturday's decider in Lisbon.
Former striker Morientes, who won the Champions League three times with Real and finished second with Monaco in 2004, said Alonso was a massive loss for Carlo Ancelotti's side.
"He offers his team good balance and has been their driving force," Morientes told FIFA.com. "He's such a crucial player so Madrid will really miss him."
Another player who could miss the final is Atletico star Diego Costa, who is a major doubt due to a hamstring injury.
While Morientes paid tribute to others, he said it was Costa and Cristiano Ronaldo who were capable of making the biggest difference.
"When you think about who could really make the difference on the night, the forwards stand out, with Cristiano Ronaldo and Diego Costa the most dangerous," he said. "But you have to appreciate the contributions made in other areas of the pitch. Sergio Ramos and Pepe are crucial at the back for Real Madrid and both are in outstanding form.
"For Atletico it's more about the midfield, where Gabi and Arda Turan have brought good balance to their play."
Morientes also praised Ancelotti for what he had achieved in less than a year with the La Liga giants, who have won the Copa del Rey this season.
"He's brought an air of calm to the team, which was needed after a period of unrest surrounding the coaching staff," he said.