The Norwegian was left demoralised following his side's late defeat against Everton at Goodison Park at the weekend.
The Bluebirds were just moments away from picking up a precious point in their fight against the drop before Seamus Coleman's last-gasp winner.
Despite City remaining in the relegation zone, three points from safety and with eight games of the season remaining, Solskjaer remains adamant that he is in it for the long-term.
"We each want to keep our place in the Premier League, but no matter what happens I will be here for the future. I can promise to be 100 per cent loyal," said Solskjaer.
"Everybody knows that continuity is the key factor to success.
"I sensed a great buzz for Wales from the start. The people are fantastic.
"The passion in this part of Wales for Cardiff City to keep their place in the Premier League seems to be confirmed day after day.
"Commitment, loyalty and hard work are values I believe are important. I have never worked as hard in my whole career, but I knew that when I took the job.
"I want to earn respect through the football my team plays and commitment to the club.
"I can promise to be 100 per cent loyal.
"This is a major project and I am committed to it.
"Right at the moment, though, my whole focus is on doing everything possible to ensure Cardiff City are still in the Premier League next season.
"We have big challenges ahead, but we are ready for those.
"Nobody at Cardiff City doubts we can keep our place in the Premier League... and we have eight cup finals in which to achieve that."