United beat Dutch side AZ Alkmaar 4-0 at Old Trafford on Thursday night to finish ahead of their Eredivisie opponents, thus securing what should be a more forgiving tie when the draw for the last-32 is made on Monday.
"We are looking to strengthen in many positions," Solskjaer said at his post-match press conference.
"We are getting there but we still need two or three players to have enough numbers."
Addressing the stark improvement in United's second half performance following a sterile first period, he added: "There wasn't any cups flying or anything [at half-time].
"We just had to get the troops together and get back to what we're good at."