Even then his heroics might still have earned a worthy Barclays Premier League point after Juan Cala bundled in a scrappy equaliser.
Cardiff felt they should have had a penalty in the latter stages when Wilfried Zaha went down under a challenge from Sylvain Distin but referee Roger East gave nothing.
Solskjaer said: "We feel very disappointed not coming away with one, maybe three points.
"It was a stonewall penalty for Wilf when he goes through two or three of them at 1-1.
"I don't know how many times we have to look at us claiming penalties and not getting it.
"We can talk about it all day long and look at the video but that doesn't help does it?
"The performance was outstanding, a phenomenal effort. They had 'cojones' as you say.
"We have given Everton a good game, so that is encouraging but we sit here with no points and we need points."
Solskjaer hailed the performance of Marshall.
He added: "He has been brilliant all season and he was outstanding again.
"The two goals he couldn't do anything about - the first goal was a deflection, the second a mishit. He was outstanding."
The result leaves Cardiff 19th in the table and facing an uphill struggle to survive in the top flight.
- Sports & Recreation
- Wilfried Zaha
- Barclays Premier League
- Gerard Deulofeu
- Sylvain Distin
- Seamus Coleman
- David Marshall