United has struggled for goals and creativity since sanctioning the exits of Romelu Lukaku and Alexis Sanchez, with the Red Devils languishing in 11th position ahead of Monday's showdown against Arsenal.
Solskjaer's side was linked to Juventus pair Mario Mandzukic and Paulo Dybala, Borussia Dortmund sensation Jadon Sancho and Athletic Bilbao star Inaki Williams before the window shut.
Speculation continues to link United with Mandzukic and Sancho, while Lyon's Moussa Dembele has emerged as another option, with Leicester City's James Maddison also a reported target in Solskjaer's pursuit of creativity.
"We let Alexis and Romelu go, you don't have to be a rocket scientist to see that it's forward that next time we're going to recruit," said Solskjaer, whose side have only scored eight goals in six games as they sit 13 points adrift of leaders Liverpool. "We're looking for some creativity and goals.
"There's no point getting players in that you're not 100 percent sure about. When you get players in, you need the right ones that are going to stay here for a longer period and that's the long-term thinking we have to show.
"I cannot think, 'I need a player because this is my reputation'. No, it's the club. There were strikers [available in the off-season], but they weren't the ones we wanted. We couldn't get the one we wanted."
While United have struggled, Lukaku has flourished since his club-record move to Inter, where the Belgian star has scored three goals to lead Antonio Conte's men to six wins from as many Serie A fixtures.
Solskjaer added: "It was time for Rom to go. He knows that. He didn't want to be here. What is the point in having players that don't want to be here?
"We need to score more goals, definitely, and that's what I've said here. We're working on improving relationships, the patterns, the understanding and we've started in one end with the foundation, we've done great defensively, but we're not happy with the return going forward.
"You wouldn't mind scoring a few goals on set-plays and from midfield, of course. I think the forwards are always going to give us goals, so of course, we both expect and hope they're going to come."