Cardiff's hopes of avoiding an immediate return to the Championship were dealt a further blow on Saturday as they went down 3-0 to Crystal Palace.
Afterwards, Solskjaer acknowledged his side, who sit six points from safety with only five games to play, require "a miracle" if they are to avoid relegation.
However, the Norwegian insists he will not throw in the towel, having taken increased motivation from Cardiff's struggles since he was appointed in January.
"I'm full of fight. I've been here three months and I've got more energy than ever and more fight in me than ever," he said.
"Every time when I was put on the bench (as a player) that galvanised me and this situation galvanises me as a manager.
"Things like this give me more fight. Things will have to happen, things will have to change and I think whoever feels those changes will know why."
Cardiff travel to eighth-placed Southampton on Saturday, with Mauricio Pochettino's men having run out 3-0 winners in December's reverse fixture.
Solskjaer is keen to gain a measure of revenge for the defeat but aware that could be a difficult ask against a team who have impressed this season.
"They're professional footballers and we've got to go out there - we've still got something to fight for and (the squad) have got to realise that," he added.
"If you do produce a miracle against Southampton, suddenly you might be back here in with a chance.
"It looks dark and gloomy but football changes (quickly). We've got to make sure I sit here and smile with you after a Southampton game that we've had a fantastic performance and result from."
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
