Spain coach Julen Lopetegui decided to omit Morata from his squad that will take on Germany and Argentina during the international break after the 25-year-old failed to score at Chelsea since Boxing Day.
Morata, however, got back to goal-scoring ways on Sunday when he netted in Chelsea's 2-1 FA Cup quarter-final victory away to Leicester, with Lopetegui going on to say there is still time for the striker to make his World Cup squad.
And Alonso, who has received his first call-up to the Spanish national side, admitted Morata was not happy at his Spain snub but insisted the striker is 100 per cent fit and focused again.
"Alvaro wasn't happy," Alonso told reporters.
"He has gone through a difficult few months with a back injury. He is now 100 per cent and the other day he scored.
"He is a very important player for us. I hope he will do well from here until the end of the season and he gets to go to the World Cup."
Alonso has a good chance of earning his first senior Spain cap in the next fortnight after being overlooked by Lopetegui despite his role in Chelsea's title-winning team of 2017.
But the defender insisted he isn't concerned with getting his first call-up to La Roja late, only on now getting to know his teammates and adapting to the team's style of play.
"Whether it's late or not, the important thing is that I'm here," Alonso added. "I'm grateful. I tried not to think too much about it.
"My focus was on doing well at Chelsea and this was a welcome surprise. This is a reward for the work I've done in recent years. I was training when I found out. I went in the locker room and all of my team-mates congratulated me. I'm thrilled and looking forward to this experience.
"I'm very focused on the next two friendlies and on adapting to the team.
"I'm eager to train and to add to this squad. More than an exam, I see this as an opportunity. I think the coach knows me well from my time at Castilla.
"It's a chance to prove myself and for me to adapt quickly to the side and hopefully, to return to the national team more times."