The Norwegian was finally relieved of his duties on Sunday morning in the wake of the 4-1 defeat at Watford on Saturday
It brings to an end a near-three tenure in charge following his appointment as temporary boss back in December 2018.
“Very, very proud. Of course, it’s one of those things you dream of in your life,” he said in a farewell interview with the club. “When you’ve been a player, when you’ve been a reserve team coach, the next job then, the only dream and the only thing you haven’t done is to manage the club, and I have now.
“It’s been a ball, it’s been absolutely enjoyable from the first to the last minute, so I have to thank all the players because since I came in, they’re top lads, top people. Some have come, some have gone, but all of them, they’ve been such an enjoyable bunch to work with.
“First of all, I want to thank the board and the owners for giving me the opportunity because it’s not for everyone and I’ve had the opportunity. I’m so honoured and privileged to have been trusted to take the club forward, and I really hope that I leave it in a better state than when I came.
“I’ve made great friends, I’ve reconnected with some great friends, new staff coming in I’ve become really good friends with. The other staff that was here when I was there, we’re good friends and we have connected and that’s what it’s about at a club like this.
“With the fans, the fans have been amazing. From day one at Cardiff until the last one now. [They’ve been] top, and we’ll see each other again.”
Laurent Blanc is one of a number of candidates to take over on an interim basis before a decision over a permanent successor is decided.
Solskjaer has endured a difficult few months and intends to return to his native Norway for a break following Sunday’s announcement.
He insists he will remain a fan of the club and wishes whoever takes over from him well.
“I’ll spend some time with my family,” he added. “That’s been probably the most difficult part, through the pandemic, with Norway being open and here being closed, my family moved back to Norway and the young one, he loves it back there, so we’ve lived apart.
“So, I’ll spend some time with them. Then, I’ll watch the team of course and hopefully, the next manager comes in and I want to support him. I want him to be successful, hopefully I’ve laid the foundations for that to happen because I know I’m good at what I’m doing.
“I’m a hundred per cent sure to create a football environment, that’s where I’m good at and at some point, I’ll probably be back [working in football].”