Instead they had to settle for another away point after their third successive scoreless draw on the road.
"When you play as well as that and don't win the game - that's what I'm disappointed about," Hodgson said after the game.
"Credit to Stoke, they defended with great gusto and determination.
"But I do have the feeling today, when you play like that and come to a difficult place to play, and having seen how we coped, I can't be anything other than disappointed we only took one point instead of three.
"I thought the referee, especially after a first half where every decision he made was contested so violently, did well to stand up to the pressure."