He also expressed his disappointment that some fans chose to chant the name of former player-boss Kenny Dalglish towards the end.
The Reds were second-best throughout and fell behind when Ricardo Fuller poked home in a scramble resulting from Rory Delap's long throw.
Kenwyne Jones wrapped things up in the 90th minute before Lucas Leiva was sent off for a second bookable offence.
"I'm sad a good run has come to an end," said Hodgson.
"It was always going to be a tough task and I knew we would be hard-pushed to win that battle but I thought we dealt well with the pressure reasonably well.
"Once they scored it was going to be an even further uphill battle.
"The first goal I am not disappointed in the manner of it because that is the manner of most goals here and that is what you have to defend against.
"For large periods of time I thought we defended it reasonably well but they got their reward from one of those.
"It would be a very unfair accusation that we lacked the mental strength or courage, as our defending from so many of the throws and set-plays proved.
"I thought today we stood up as well as we could be expected to considering the pressure we were under.
"I don't think the players threw the towel in and never looked like throwing the towel in."
Asked if the singing of Dalglish's name disappointed him he added: "I suppose it does. That seems like it is going to be part of life at Liverpool.
"I think we are trying to do the best job we can in the circumstances and I don't know that that type of singing helps anyone.
"But I didn't hear it and I am sure there are lots of fans who sympathise with us and what we are trying to do."
Hodgson felt the Reds suffered in the second half because striker Fernando Torres carried on playing despite injury, although he played down the seriousness of the problem.
"He didn't want to come off and I didn't want to take him off but he was not firing on all cylinders," said the 63-year-old.
"We offered him the chance to come off but he wasn't interested in that.
"I don't think it was too serious, if it had have been I don't think he would have carried on but it was a nasty knock which he took on his ankle."
Stoke boss Tony Pulis, whose side moved out of the bottom three and up to 10th - a place above Liverpool on goal difference - felt their tactics were spot-on.
"We are very pleased. The important thing was to push up on Liverpool and stop them getting a rhythm in their passing and we really closed them down from the front.
"I am very pleased with everyone in my team. In a three-game week when you have to play a top side at the end of that week it is always very difficult.
"We showed loads of passion, commitment and energy and they deserved their victory."