The Potters took the lead at the Cardiff City Stadium in first-half injury time when Marko Arnautovic scored from the penalty spot.
Referee Howard Webb gave the spot-kick after deeming that Peter Odemwingie had been brought down inside the box by Cardiff defender Kim Bo-Kyung.
The hosts themselves were awarded a penalty in the early minutes of the second half when Steven Nzonzi committed a foul on Fraizer Campbell.
Peter Whittingham made no mistake from 12 yards, while just before the hour mark Juan Cala had a goal correctly ruled out.
The Premier League match eventually finished in a 1-1 draw, leaving manager Solskjaer claiming that Stoke's penalty should not have been given.
"I think it is a good point," he told Sky Sports. "I think if you look at the game as a whole, then a draw is what we both (Cardiff and Stoke) deserved.
"I have just been shown the first penalty and I agree with my first thought - it is not a penalty.
"I have not seen ours, so I cannot comment on it. It is difficult for a referee to make the decisions right then and there and you just have to accept them.
"We all thought we had got the vital second goal but it was correctly ruled offside, I think."
Cardiff remain in the relegation zone, two points from safety with three more games remaining.
The Welsh outfit will take on Sunderland (A), Newcastle United (A) and Chelsea (H), and Solskjaer believes that they still have a chance of survival in the Premier League.
"We have got two cup finals, but we have to focus on Sunderland as we are two points of Norwich," said the 41-year-old.
"The boys have got a never-say-die attitude and we are looking forward to our next three games."