The striker, who turns 20 on Sunday, netted the Baggies' second goal of the evening with Markus Rosenberg and Nicolas Anelka also on the scoresheet after the Greek Superleague outfit took an early lead.
"Saido did exceptionally well," said Downing to the WBA website. "I know what he's like after five years or so of working with him. He's showing some good potential. He's got some good players around him.
"Nico is helping him. The boy is just learning his trade. I'm very conscious of young players getting thrown into the limelight.
"It's important that we keep his feet on the ground and make sure that he's learning every day.
"He's a very level-headed boy and I'm sure he'll understand that. If you ask him, he is just taking every day and every training session as it comes.
"He's progressing very nicely."