The Bluebirds showed early promise, but ended up suffering their biggest home reverse since Cambridge United plundered the same scoreline at Ninian Park back in April, 2000.
A four-goal hiding against another bottom-half club was not what was expected, or needed, as the season reaches crunch time, and left Solskjaer pondering what might have been.
"You get the first goal, it's a different game," said the beleaguered Norwegian, whose side are languishing 19th in the Barclays Premier League table - three points from safety.
"We didn't, and that changed the complexion of the game. That's how it is.
"We just weren't good enough in the two boxes. If you don't take your chances and they are efficient and score the other way, you've got to hold your hands up and say you don't deserve to get the better result.
"I think everyone realises where we're at, and what situation we're in, and you can't hide the fact that we lost against a team in and around us and they've gone away from us now.
"It's going to take a momentous run to catch some of the teams.
"The only way I know how to get out of disappointment is to work hard, look forward, do the right things, not make rash decisions."
Cardiff failed to give owner Vincent Tan - who is 62 on Sunday - any kind of birthday present.
A deflected shot from Tom Huddlestone, a brace from the clinical Nikica Jelavic and a goal on the counter-attack from Jake Livermore sealed it for the visitors.
Solskjaer added: "It's not the best birthday present to give him (Tan), is it? And it's mine on Wednesday, so of course we wanted to get three points here.
"The third goal was the one that stopped the belief that we were going to get anything positive out of the game, but what I will say is that we still kept at it, the lads never got their heads down and stopped trying.
"That's a positive thing - even though you're 4-0 down you still try to get something out of the game, a goal for a player or chances, and we did create chances."
Solskjaer felt his players gave the likes of Croatian marksman Jelavic too much time and space, but he praised Steve Bruce's side.
"They defended really well and were really efficient," he said.
Bruce was delighted with the performance of his new strike partnership, Jelavic and Shane Long, who linked up throughout and always looked dangerous.
He said: "I didn't think we played particularly well in the first half. I thought we gave the ball away too cheaply, but what's got us the win is the little bit of quality we've invested in up the top end of the pitch.
"When you're not playing particularly well and you've got two like we've got, you're a threat.
"That, for me, was the big difference in the whole game - that ability to score a goal and with these two in the team; we've all of a sudden got it."
The tables have turned for the two clubs, who were both promoted from the Championship automatically last year. Cardiff's cushion last May has not translated into any dominance this season, and now the Bluebirds are the ones struggling, unable buy a goal.
Bruce is well aware of the competition in the Premier League, though, and knows the survival job is nowhere near done.
"In this league you can quite easily go six without a win," said Bruce, whose side now have eight victories this term. "You can quite easily go six to eight weeks.
"For a newly promoted team the players have got a fantastic hunger to be Premier League players. I've always said from day one you need 10 wins, and you're always going to get a few draws."
Cardiff have reportedly scrapped plans to travel to Abu Dhabi for a training break in the coming week, following their heavy defeat.
Solskjaer will keep his players at home, the BBC said, and work towards next weekend's tough-looking league match at Tottenham.
"We've just got to work hard," said Solskjaer. "It's not going to be easy to go to Spurs next Sunday.
"We have an extra day to prepare for that game and we are going to be prepared."