McClaren, who led the Magpies to six wins in 28 Premier League matches, was replaced by Benitez in March, but the Spaniard could not prevent them from being relegated to the Championship.
"I conceded too much, especially early on, instead of saying 'we need this and this'," McClaren told BBC Radio 5 live.
"I hope they've allowed [Benitez] control of everything."
He added: "Listen to him, this is what he wants, these are his requirements, this is the team he needs to make."
Newcastle sat 19th in the table when McClaren departed, with a 3-1 home defeat by Bournemouth his final match in charge.
"The mistake I made was I compromised too much," said the former England, Derby and FC Twente manager.
"I wanted to get enough results on the field so I could gradually gain a bit more control. But I think you have to be domineering as you go in, you have to make sure you get what you want."
The 54-year old is confident the Magpies have learnt from his experience and will afford Benitez greater control as he bids to return Newcastle to the top flight.
"I think now with Rafa being in there he will be allowed to take control of media, of staff, and of recruitment - which is the most important thing," he said.
"You have to make sure that you work together to establish what you want, what you're comfortable working with."
Ex-Newcastle United boss Steve McClaren hopes new manager Rafael Benitez will be allowed greater control at the club.