The Baggies legend was surprised by Saturday's news.
"I am shocked - I didn't see that coming at all," said Regis to the Birmingham Mail.
"If you're looking at the bigger picture then I thought he might get longer but it shows the pressures of staying in the Premier League with the new TV deal.
"Certain players haven't come to the level that was expected either, which didn't help him.
"Martin Jol would be a strong candidate. He knows the club, he knows the continental system Albion have in place and he'll know the parameters Albion work under because he had them at Fulham.
"He's managed at the top level across Europe so he ticks many boxes."
Regis added: "I think with the position Albion are in they need a 'been there, done that' manager.
"It needs someone with experience to stop the slide."