Shelvey appeared to have sealed the game as a contest with a sublime free kick before Balbuena pulled one back for West Ham and Snodgrass volleyed home in the 90th minute, forcing Newcastle to defend desperately in stoppage time.
West Ham are now 13th in the table with a balance of 3 wins, 4 draws and 4 defeats in their 11 Premier League games. They haven't won since the 22nd of September, when they played Manchester United at home, where Solskjaer also starts to raise doubts after his bad start to the season.
The 27-year-old scored a free-kick and was heavily involved in Newcastle's other two goals as he made a real statement of intent to Steve Bruce.
West Ham travel to Burnley on Saturday and will hope to get things right, and Pellegrini could be forced to ring the changes.More news: House Republicans Request Hunter Biden Testify in Public Impeachment Hearing
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"It's really hard to understand why we started the game with that attitude and without the pace that we need to win the game", he told the club's official website.
The Red Devils are in tenth place in the Premier League table and a staggering 10 points adrift of fourth-placed Chelsea FC after 11 games this term.
Pellegrini is at a loss as to how West Ham have gone from beating Ole Gunnar Solskjaer's side in September to losing 4-0 against Oxford in their next match - the first of their six-game winless run.
The home fans jeered the players both at half-time and full-time in the game against the Magpies at London Stadium. Newcastle had a couple of chances first half that Roberto saved but we need to have a good meeting to review what we are doing.