United produced an abject display against Sean Dyche's men on Thursday (AEDT) as it lacked a cutting edge in attack without the injured Marcus Rashford, who could be out until April with a back problem.
Chris Wood and Jay Rodriguez got the goals for Burnley, who ultimately had little difficulty hanging on to the victory.
United have been strongly linked with Sporting CP midfielder Bruno Fernandes, though media reports continue to suggest the two clubs are well apart in their valuation of the Portugal international.
Solskjaer is adamant United are looking to bolster the squad, though he failed to answer whether he feels appropriately backed by the club's board.
He told said: "We are looking to improve, we have got our targets. Days like this highlight how well some of them [the young players in United's squad] have done so far this season – some of the results and performances have been fantastic.
"This is our second defeat at home and first since August. I thought we had turned that corner, winning games like this, but we haven't, clearly.
"[Transfers] are always going to be the talk at the moment. We have started a clear out and get-players-in job, now it's the transfer window so I'm going to be answering these questions until it closes. We are working on things.
"For me the most important thing is we have to perform on the pitch. Today wasn't good enough for a Manchester United team."
The defeat left United six points adrift of Chelsea in fifth, level with Tottenham and Wolves on 34 points.