Referee Howard Webb chose to point to the spot late in the first half when Peter Odemwingie, making his return to former club Cardiff, went down under a clumsy challenge from Kim Bo-kyung.
Marko Arnautovic fired Stoke ahead from 12 yards, but the hosts secured a point courtesy of a penalty of their own in the 51st minute, scored by Peter Whittingham.
Solskjaer believed Kim was unfortunate to be penalised for his challenge on Odemwingie, but said his players were "galvanised" by the setback.
"I still feel what I felt at the time - that it's not a penalty - but I accept Howard has to make a decision there and then," said the Norwegian.
"He hasn't got an advantage of all the replays we have but, for us, of course 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 try to control your emotions because that's important when you get decisions like that against you.
"They (Cardiff's players) felt hard done by. They were there very close to it and they said let's just make sure we use this to gain some momentum and get some energy."
While Cardiff were able to rescue a draw, they are two points adrift of safety ahead of the Premier League's 17th-placed side, Norwich City, hosting leaders Liverpool on Sunday.
Solskjaer is hoping two victories from games against Sunderland, Newcastle United and Chelsea can prove enough to secure survival.
"Two wins I think would be enough, but then again you never know in this league," he added.
"You never know what the outcome is going to be in any of the games.
"We still believe in Easter miracles - it'll be one of those (where) you raise from the dead but it's not a miracle needed, but two very good performances."
