Another costly defeat on Saturday saw Cardiff stranded in the Premier League relegation zone, having won just one of their last 11 league games.
Eight defeats have come during that period, with the home loss to Steve Bruce's side representing another low point in their campaign.
Strikes from Tom Huddlestone and Jake Livermore either side of Nikica Jelavic's double were enough to ensure that Hull left the Cardiff City Stadium happy.
Such jubliance was in stark contrast to the emotions felt by Solskjaer, who has now challenged his side to win five of their remaining games to guarantee their Premier League survival.
He said: "We won't lie down and give up. We were knocked back today, but we'll keep working hard and stick together."
The former Molde manager remains confident that his side can get out of trouble.
"It will take a monumental run to catch some of the teams," he added. "We need five wins from the last 11; we need 15 points.
"I still think we can get them and be in the Premier League next season. We hoped to get one of those wins today so we need to find it somewhere else now."