Joey O'Brien's strike two minutes into the second period cancelled out Jonathan Walters' first-half strike, but try as they might they could not get that elusive winner which would have seen them go to fifth.
"I thought we deserved three (points) in the end," Allardyce said.
"Stoke were slightly better than us in the first half and we had to recover from what was an extremely good goal.
"Having to come from 1-0 down in any game in the Premier League is difficult.
"(It's) another point on the board, we move on reasonably happy."