The former Manchester United hero has found victories no easier to come by than his predecessor and now faces a home game against Hull City, who were promoted with Cardiff last May and are five points above them.
"We need to get points now," Solskjaer told a news conference. "Thirty-seven points should do it. So five more wins. But it can suddenly change. If we can get a good result here, you're looking at the next two home games in a confident manner.
"We need to get wins back to back now, we can't wait four or five games for the next home win."
The bottom half of the Premier League remains congested, with only eight points separating 11 teams and even Cardiff's Welsh rivals Swansea, who are in 10th place, not out of danger.
(Writing by Steve Tongue; editing by Clare Lovell)
