It appeared to be a harsh decision by referee Howard Webb, who punished Kim Bo-Kyung for his challenge on former Cardiff player Peter Odemwingie, while the Bluebirds also saw a later Juan Cala effort ruled out for offside in the 1-1 draw.
The result kept Cardiff in the relegation zone, but they are now just two points behind Norwich, who host title-chasing Liverpool on Sunday.
"I felt what I felt at the time, that it was not a penalty, but I accept that Howard has got to make a decision there and then," Solskjaer said.
"He (Webb) hasn't got the advantage of all the replays that we have.
"For us, it galvanised everyone in the dressing room
We felt hard done by.
"I didn't have to say a lot at half-time, apart from maybe trying to control the emotions, because that is important when you get decisions like that against you
You can't make him change his mind.
"The players were very close to it, and the players said 'let's make sure we use this to gain some momentum and get some energy'.
"The way we came out second half and put them under pressure, got the goal, got a disallowed goal, got the crowd going - they were fantastic again - and it was just what we wanted.
"But then again, they (Stoke) took over the last 10 or 15 minutes.
"The first 75-80 minutes I thought we deserved maybe more than a draw
Towards the end, you might just say we didn't deserve anything.
"But we have got a top, top goalkeeper, and he saved that point for us.
"We lost the momentum
We had so much of it, especially the first half-hour
We were getting a bit anxious towards the end, and they had chances.
"The chance 'Marshy' (goalkeeper David Marshall) saved (from Oussama Assaidi) should have been a goal, and we should have sat here with no points, but we have to thank him again."
Cardiff head to fellow strugglers Sunderland next weekend, which is followed by an away clash against Newcastle before their season finale at home to title-chasing Chelsea on May 11.
"Two wins I think would be enough, but then again you never know in this league
You never know what the outcome is going to be in any of the games," Solskjaer added.
"We are two points behind Norwich
We've got to have one more win than them in the last three games and get more points than Fulham and Sunderland.
"It is not a miracle needed, but it is two very good performances needed in the next two games to give us a chance in the last game against Chelsea."
While Cardiff face a continued fight to avoid a quickfire Championship return, Stoke can reflect on just one defeat in their last eight games that has helped secure mid-table comfort
"The neutrals in the ground would think they were a couple of soft penalties," Stoke boss Mark Hughes said.
"I am not going to surprise you by saying I thought ours was a valid penalty and rightly given.
"My view on Cardiff's penalty is that it was very soft and the lad has looked for a movement from Steve N'Zonzi that would allow him to go down.
"I think he was always looking to go down in that situation - he drew the movement from Steven
There was very minimal, if any, contact, and it is difficult for Howard Webb when players go down in those situations.
"That was the only period in the game where Cardiff created a bit of momentum and created some opportunities for themselves.
"In the second half we were in the ascendancy from Assaidi, which if we had converted that chance it would have won the game for us.
"But we will take the point."
Source : PA
Source: PA