The limp defeat leaves Newcastle second bottom of the Premier League table with just 24 points and staring another relegation in the face.
McClaren spent heavily in January to bring in the likes of Jonjo Shelvey and Andros Townsend in a bid to save themselves from the dreaded drop.
'A mess from top to bottom'
But after the club's latest defeat a visibly agitated Shearer launched a withering attack on McClaren, his status at St James' Park and the club's 'bizarre' hierarchy on BBC's Match of the Day.
"He's (McClaren) in massive trouble," Shearer told MOTD.
"He has to take his fair share of the blame.
"But the whole club is a mess from top to bottom.
"There's no statements of intent on the pitch when it really matters.
"They've got no academy players coming through.
'Chief scout holds too much power'
"The chief scout Graham Carr holds all if not most of the power with players coming in and coming out.
"The team lacks characters and leaders.
"He's not a "manager" at Newcastle, I'm not so sure he has all that say on players coming in, coming out.
"He's also on the board which is another bizarre decision."
Shearer knows a thing or two about seeing his beloved Newcastle relegated.
The club's all-time top goalscorer had an eight-game spell in charge at the end of the 2008-09 season but could not get the wins needed to keep them up.
Opinion will resonate with fans
His opinion still carries a lot of weight in Newcastle, though, and his opinion on the club's setup is sure to resonate with Magpies supporters.
Fans were outraged by the Bournemouth performance and left in their droves before the final whistle, hurling abuse at players and the bench alike.
And things don't get any easier for McClaren's men with a trip to Premier League leaders Leicester City next up before a crunch Tyne Wear derby with relegation rivals Sunderland.