The Celtic skipper, 32, stepped down from Scotland duty for the second time last month, citing the need to “look after my own body”, and 59-year-old McLeish could not persuade him to remain available.
“It was on the cards,” McLeish said. “I totally respect Scott for what he’s done. It would’ve been nice to have had him continue, with the tactical nous he has and the way he’s really improved as a footballer.
“You can’t beat experience and we will miss Scott but hopefully we’ll find a replacement.
“I really felt that his mind was made up – it didn’t matter who was in the job. Even if Gordon [Strachan, McLeish’s predecessor] stayed, perhaps he would still have made this decision, because Celtic have shown great confidence in him in awarding a new contract.
“And I think sometimes Celtic would only get three-quarters of Scott Brown and Scotland would only get three-quarters, instead of the full 100% of Scott Brown.
“He says he’s feeling it in his body now, and I think he’s getting to that stage of his career where he wants to give everything to his club.”