Solskjaer's only previous experience of Premier League management came in 2014, but he was unable to keep the Bluebirds up as he lost 12 of his 18 matches in the top flight.
Speaking to Sky Sports' Adam Bate, Solskjaer reflected on his time with Cardiff and said joining them "wasn't the right decision."
He replaced Jose Mourinho at Old Trafford in December, and has won nine of his first 10 games.
The Norwegian feels his prior experience of United as a player has helped him do a better job:
"This is a completely different club and situation to come into. I know the culture and identity of the club and the playing style. Manchester United, of course, suits me a lot more than a club that struggles towards the bottom of the table. I wasn't ready for that fight. I didn't say I wasn't ready for the Premier League. That's different."
"I was more prepared for this one," he added. "It is easier here because I know what the DNA and identity of Manchester United is and what a Manchester United player is."
Solskjaer has changed the situation at Old Trafford dramatically in a short space of time:
Prior to his arrival, United had already lost five times in the Premier League and been knocked out of the Carabao Cup by Derby County.
Solskjaer has adopted a much more positive approach than his predecessor, which he believes fits in with United's identity:
"It's a winning identity. It's a confident identity. We want to take risks. We want to go for the second, the third and the fourth goal because that's just how we do things at Manchester United. If you can't handle that then you are at the wrong club."
He has also sought to restore counter-attacking to United's game and has used past examples—such as a devastating break from Wayne Rooney, Cristiano Ronaldo and Park Ji-Sung against Arsenal in 2009—to educate his players (h/t Rich Fay of the Manchester Evening News):
Marcus Rashford has benefited from Solskjaer's appointment, as he showed on Saturday with the decisive goal in a 1-0 win over Leicester City:
"Whether it is back home with my daughter's team or it's this, I just love working with footballers who want to improve," Solskjaer said. "I love speaking to them and giving them my help and my thoughts."
Solskjaer's desire to get the best out of his players is helping them realise their potential, as they had been performing well below their capabilities under Mourinho.
Though there are some limitations in their squad that will need addressing in the transfer market—most notably in defence and wide positions—they're perhaps not as far off their rivals as it seemed a few months ago.
That's the case in terms of the league table, too, with United now in fifth and two points off the top four.
If Solskjaer can maintain their excellent run until the end of the season, the Red Devils will have a strong platform to build on for the next campaign.