Elliot's string of fine saves allowed the Magpies to sneak away from the south coast with a 1-0 victory, their first win on the road since January.
The 29-year-old overcame thigh trouble to ease Newcastle's goalkeeping crisis, with Tim Krul out for the season and Karl Darlow still recovering from ankle trouble.
Darlow is expected to be fit for the trip to Crystal Palace on November 28, but McClaren could well now keep faith with Elliot.
"He's the man in goal at the moment and we'll wrap him in cotton wool and try to get him out there for the next game," said McClaren.
"It's a squad game. When we lost Darlow and Tim Krul we turned to Rob Elliot.
"He's been terrific from day one, good around the place, experienced, a good talker and he won us three points at Bournemouth."