While United have tightened up at the back with three clean sheets in those outings, a lack of goals is a growing concern for Solskjaer after a performance that former captain Gary Neville called "boring".
Man City look near-certainties for the title as they lead second-placed United by 14 points, while recent results leave United looking over their shoulder as the likes of Liverpool and Chelsea - who face off at Anfield on Thursday - looking to make a late play for Champions League qualification.
"It's not good as you know if you want to move up the table, you need to win," the Norwegian told the BBC.
"You have to earn the right, you have to win tackles, you have to fight you have to play passes better as we kept giving the ball away.
"We go into every game thinking we need to win and we want to win. We just have to concentrate on ourselves. We know we're in a fight to be in the top four so every game is important."
Additional reporting by Reuters.