Smith is looking to bow out of football management at the end of the season with a third consecutive Clydesdale Bank Premier League title, despite being unable to buy a player for a two-year spell. Assistant McCoist has been groomed as his successor since both gave up jobs with Scotland to return to their first love.
"Obviously Ally has a reputation of being a fun guy but when it comes to football he is very serious," said Walters, who was back in Glasgow promoting ESPN's live coverage of the SPL clash between St Mirren and Rangers on Sunday.
"He knows his stuff, he is a good coach and he is aware of what Glasgow Rangers means to the supporters, which is a really important thing.
"Having worked under Walter, he must have learnt loads of stuff. He is a young man in terms of experience but he should definitely get a chance to show what he can do and I think he'll relish it."