Stand-in manager McAllister visited Houllier, who has been suffering from chest pains, in hospital and spoke to the Frenchman before the game.
Bent, one of Houllier's January signings, scored his seventh goal in 12 games after Kenwyne Jones had given Stoke the lead.
McAllister said: "A few of the staff went to see Gerard on Saturday morning. I saw him on Friday night.
"I spoke to him before the kick-off and his main concern as always was the players. He wants them to do well.
"I'm going to go up to the hospital now. All the signs are encouraging. He has got a bit of colour in his cheeks and he doesn't look like a guy who has had a tough couple of days."
Source: PA
Source: PA