The hosts had twice taken the lead through strikes from Jordon Mutch and Fraizer Campbell either side of Luis Suarez's 16th-minute effort before Martin Skrtel equalised prior to the break.
And with Mutch and Kevin Theophile-Catherine off the pitch receiving treatment, Skrtel edged Liverpool in front nine minutes after the restart, before Suarez and Daniel Sturridge added a goal each to put the game to bed.
While Mutch added his second of the day late on, Suarez completed his hat-trick deep into injury time, leaving Cardiff boss Solskjaer bitter over his lack of available defenders for Skrtel's second.
"We're disappointed that you don't get anything out of the game that you had for the vast majority of the first half," he said.
"I thought (the) first half was excellent from our side then I think you should look at that rule - how can you defend a corner kick with nine men?
"Two of your men - they've not faked anything, they've not dived - they just want to get on the pitch, the two of them at the same time.
"I said to the fourth official: 'They're going to score here, don't worry about that'.
"So you've got to look at that, for me."
Solskjaer, whose side were helped by the rest of the bottom five all tasting defeat on Saturday, remain three points off safety in 19th place.
And although the Norwegian was pleased with the performance Cardiff put in against title contenders Liverpool, he called for a change to the rules regarding players receiving treatment.
He continued: "I don't want to sit here and sound like an old grumpy man but what if another two or three of mine went down - do you think that should happen?
"You've got to look at the rules but we can discuss it all day long - I knew they were going to score.
"You've got two of my biggest men - Jordon Mutch and Kevin Theophile-Catherine - out of that corner kick so where that common sense is (I do not know).
"You can hide behind all the players who dive and want to have treatment to waste time - of course they're not going to waste time.
"Then again, rules are rules aren't they?"