United are thought to have contingency plans in place should that scenario arise but the possibility of having to play six Europa League qualifying matches in the space of six weeks just to reach the group stage would be another huge setback to Solskjaer at a time when he is facing a huge rebuilding process.
"We're all disappointed we're not in the Champions League but that's a true reflection [of where we are] and the table seldom lies at the end," the United manager said.
"We gave ourselves a chance to be in the Champions League, we had so many opportunities to be third or fourth and weren't able to take them.
"The Europa League next year is the right place for us and if City don't win the FA Cup, we'll have an early and bright start for the Europa League qualifiers and that'll make it more difficult.
"It's not what we want but let's see what happens with Arsenal and the final with City but that's the reality. The kids will get chances to play games. I'm an optimist, you will have to make the most of it.
"We haven't taken enough points, won enough games, scored enough goals. It shows us where we are. We're not living in fantasy land thinking we can catch the top two [Liverpool and Manchester City]. We're far away but we shouldn't be speaking about being far off the top four at Manchester United. We're many levels [behind] at the moment. That's the size of the challenge, it's a great challenge for us but I'm sure we'll make it."
Alexis Sanchez's Old Trafford career hit another low when he was substituted after 54 minutes with a twisted ankle on his first start since March 2.
It raises the prospect of Sanchez having played his last game for the club, even if United may struggle to offload their £500,000 a week misfit unless they subsidise a transfer.
But asked if the Chile striker had played his last game for United, Solskjaer refused to discuss Sanchez's situation directly but admitted there were various players who fans may not see again.
"There's a chance you've seen the last of [a number of] players, always a chance, but I wouldn't say that about any individual," he said.
"[Yesterday] wasn't about one individual that was disappointing, it was the whole team. The players were running, they were trying but we just weren't good enough."
Former United captain Gary Neville was scathing in his criticism.
"This is not a team. The more I watch this, it's not a team," Neville said. "Ole Gunnar Solskjaer needs to dismantle this [team] piece by piece.
"Is that the last time we see Alexis Sanchez in a United shirt? Walking down the tunnel at Huddersfield?
"Nothing about this United team I like at all. They're just awful. They are a despondent group of people. Solskjaer is smiling at them, they're that bad."
There is uncertainty over the futures of up to 10 players. Antonio Valencia will leave when his contract expires, Ander Herrera is due to join Paris Saint-Germain as a free agent and Juan Mata has yet to agree a new contact.
Matteo Darmian and Marcos Rojo are also surplus to requirements and United are expected to listen to offers for Sanchez, Eric Bailly, Romelu Lukaku and possibly Andreas Pereira. David De Gea is about to enter the final 12 months of his contract and has still to sign a new deal, although United insist the goalkeeper will not be sold this off-season.
