Blues striker Morata scored his first goal of 2018 in the FA Cup quarter-final win over Leicester City on Sunday, ending a run of 13 games in all competitions without scoring.
The 25-year-old's dip in form, combined with a back injury, saw Antonio Conte experiment with Eden Hazard as a false nine and use January arrival Olivier Giroud in place of Chelsea's record signing.
Alonso admits it has been a tough time for his compatriot but he is confident the former Real Madrid man, who was overlooked by Julen Lopetegui for this month's friendly matches, will enjoy a strong end to the season.
"Alvaro wasn't happy," Alonso told a news conference. "He's gone through a couple of difficult months because of a back problem. He's at 100 per cent now, he got back to scoring the other day...
"I hope he helps us at the end of the season. He's really important and I hope he's at the World Cup."
Alonso could earn his first senior Spain cap in Friday's friendly with Germany, having earned a spot in Lopetegui's squad thanks to his form for Chelsea.
The 27-year-old insists he was never unduly distracted by his international prospects, despite his long wait to join the senior squad, but he now wants to make the most of his chance.
"I tried to give it the least importance," he said. "My job was to do well at Chelsea and to be focused on the team's goals.
"It came as a surprise and a prize for the last few years. Now, I'm quickly getting focused, and it's really exciting.
"It's more than a test. I take it as an opportunity. The boss knows me well from my time with the youth team. It's an opportunity to show, to adapt quickly to the team's play and to earn a call-up many more times."