Solskjaer and the Red Devils have only taken 10 points from their last seven league games.
On Sunday, they fell further away, following a 1-1 draw at West Brom.
Despite returning to second place on goal difference, they have ultimately slipped further behind local rivals Manchester City.
Pep Guardiola’s side are now seven points ahead at the top of the table and have a game in hand, but Solskjaer insists Man Utd will not be letting them get away too easily.
He said: “No one will give it away this early. This season is so unpredictable, life is so unpredictable, anything can happen and of course we’re not going to settle for second.
“It’s a compliment to the boys that we’ve gotten ourselves into the position we’re in. We’re the team closest [to Man City] and we should be challenging the team in front of us.
“We’re not going to let them get away with it, but we need to win games to be in that position.”