Pizarro signed for Miami in February after a bitter negotiation that ended with Monterrey lodging a complaint with FIFA. The player was adamant that moving to MLS and being associated with David Beckham would help his chances of one day playing in Europe.
They are sentiments Alonso agrees with.
"What MLS can give him that Liga MX didn't, or didn't as much, is that shop window to [clubs] abroad," said Alonso in an interview with ESPN's Fernando Palomo. "MLS is watched a lot more abroad [than Liga MX]."
Alonso coached Pizarro at both Pachuca and Monterrey and said the 26-year-old has the quality to play in Europe and that being outside of Mexico helps him.
"[MLS gives Pizarro] the possibility of gaining experience, competing in another league with other types of difficulties so he can show how capable he is," Alonso said.
Lozano has struggled for minutes at Napoli this season since Gennaro Gattuso took over as coach, but Alonso is backing him to overcome the hurdle because of how competitive he is.
"I'm convinced that Lozano is doing everything, redoubling his efforts and he has to keep going and working and the rewards will come," said Alonso. "The coach will see [his hard work]. There is no coach in the world that doesn't put on the best player on the field. It's impossible.
"There are situations in your career in which you have to take big steps and grow and I'm convinced 'Chucky' will do it because he's an animal for competition, he loves to compete, he won't give in."