Cardiff had spent a lot, extremely poorly in the summer between their promotion and the start of the Premier League season. The atmosphere in the club then turned toxic incredibly quickly, with McKay's dismissal and racism scandal, and widespread rumours of interference in footballing matters from the owners.
Solskjaer was brought in after the January window had opened, given no time to evaluate the squad, but then tasked with sorting the team out on a shoestring budget. Ultimately, they weren't good enough when they were promoted, didn't sign the necessary quality to improve enough before the season, then imploded somewhat mid-season, leaving whoever came in next with an almost impossible task.
After they were relegated, they lost a lot of players, and he basically had to rebuild the entire squad, but with a fraction of the transfer budget McKay had been afforded the summer before.
At the start of the next season, they won two of their first three games, drawing the other, but then went four games without a win, losing three and drawing one. Solskjaer was then sacked, just 7 games into a 46 game season. However, the three games he lost were to Norwich, who finished four points off the winners in third, and won the playoffs, Middlesbrough, who finished just a point behind Norwich, and Wolves, who missed out on the playoffs on goal difference, finishing level on points with both Brentford and Ipswich, who rounded out the other playoff teams behind Middlesbrough. All were strong sides, and they lost two of the games by a single goal. Later in the season, after he'd been sacked, they went on a run of thirteen games with only one win, losing six of them. They were just a poor side expecting far too much, far too quickly.