The London club have won plenty of plaudits for their free-flowing forward play so far this season, but they had to abandon those principles to claim a 2-2 draw at the Britannia Stadium.
West Ham deservedly trailed Stoke at half-time thanks to Victor Moses' first Premier League goal in almost 14 months and they were two down early in the second period following Mame Biram Diouf's header.
But Enner Valencia pulled one back within four minutes, with West Ham's first shot on target, before Stewart Downing levelled with a powerful strike with 17 minutes left.
Allardyce's men came into the game fourth in the league having won all of their previous three matches, including success against champions Manchester City last time out.
But they looked a shadow of that side without injured star striker Diafra Sakho and Allardyce was forced into fundamental changes having seen how his side struggled against Stoke's pressing.
"I had to tell the players to change the game today," the West Ham manager told reporters.
"They wanted to play our passing game, the way we have been playing recently up to now and with the wind and with pitch being a bit bobbly and with Stoke closing us down, it simply wasn't working."
"At 2-0 it was about changing the shape of the team and getting the substitutes on that were going to give us an opportunity to get back in the game and find out whether Stoke knew how we were going to play.
"We kept Stewart Downing in behind and put Enner Valencia up front with Carlton Cole and we said to the players 'You have got to start moving the ball forward a bit quicker'.
"That quality shone through in the end.
"The two goals we scored were fantastic goals. That extra quality that we have got this year has paid dividends today, when it looked like we were going to get nothing out of the game.
"We have got a very precious point. A point that has been well-earned maybe not deserved.
"That's the way Premier League is but shows the character of our team."
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