Seamus Coleman's 93rd-minute winner settled Saturday's Premier League clash at Goodison Park as Cardiff came agonisingly close to clinching what would have been a vital point in their battle to avoid relegation.
Gerard Deulofeu earlier gave Everton the lead after 59 minutes before Juan Cala levelled nine minutes later.
Cardiff saw appeals for a penalty waved off by referee Roger East after Wilfried Zaha looked to have been toppled over by defender Sylvain Distin.
The decision left Solskjaer to bemoan: "We are really disappointed that we have not come away with one or maybe three points.
"It was a stonewall penalty for Wilfried when he goes through between two or three of the defenders when the game is 1-1.
"And that's now I don't know how many times we have to look at us claiming a penalty and not being given it, so it's about time now."
Defeats means Cardiff are second bottom and Solskjaer added: "This is not the reason we lost, but it is a stonewall penalty. The decision should have been a certainty.
"He (Zaha) weaved his way through three or maybe four defenders and I think he is tripped up by Distin. We can talk about it all day long and look at the video, but it doesn't help us, does it?"
Despite the defeat, Solskjaer was full of praise for his side's display, singling out goalkeeper David Marshall in particular.
He said: "David Marshall has been brilliant all season.
"He was outstanding again, the two goals he can do absolutely nothing about. He was outstanding.
"The performance was outstanding, it was full of team spirit and we created chances.
"We came to a difficult place as they have only lost once here. We have given Everton a good game and that's encouraging, but we still sit here with no points and we need points."
