"To my mind, Neil deserves a knighthood for getting someone to pay £12.5m for him," said Shiels.
"Any time we played Celtic I'd tell our lads not to worry about him being on the ball as he doesn't keep it very well.
"We found that, when you gave him space, he just didn't have the natural instincts to know what to do with the ball. We would press players like Joe Ledley and Charlie Mulgrew but we just dropped off Wanyama and, most of the time, we got the ball back from him.
"Celtic have made a big financial gain from his transfer but I don't think they've been weakened in a footballing sense."