Solskjaer admitted that they have themselves to blame.
United drew 1-1 with relegated Huddersfield on Sunday, which saw them miss out on a top-four place and the Champions League next season.
It is the third time in six years United have failed to make the Champions League after-Sir Alex Ferguson’s departure as the club’s manager.
“We gave ourselves a chance to be in the Champions League, had so many opportunities to be third or fourth, but weren’t able to do it,” Solskjaer told Sky Sports.
“Maybe it’s the right place to be for us, the Europa League next year.
“If City don’t win FA Cup we’ll have an early and bright start for EL qualifiers and that’ll make it more diff.
“We’ve been inconsistent throughout this season, good periods and very bad periods, and it’s just caught up with us. It’s a fair reflection, being sixth.
“It’s been a tired team towards the end of the season. When you get bad results you lose energy and start worrying and that’s caught up with us.
“It’s not what we want, but then again you can use the Europa League as something positive, as Chelsea and Arsenal have done and as we did a couple of years ago.”
Alexis Sanchez went off injured in the second-half and Solskjaer was asked if that was the £500,000-a-week forward’s last appearance in a United shirt.
“I can’t talk about individuals now, but there’s a chance you’ve seen the last of players, always a chance, but wouldn’t say that about any individual,” said Solskjaer.
“Today wasn’t one individual that was disappointing, it was the whole team.”
Scott McTominay put United ahead after eight minutes, but a mistake by Luke Shaw allowed Isaac Mbenza to equalise, with Solskjaer’s side unable to find a winner.
Former United defender Gary Neville was scathing in his assessment of his old club and said: “This is Huddersfield Town who have struggled all season.
“Watching this Huddersfield team, they haven’t got the quality, but I like watching them a lot more than watching the ones in the red shirts, to be honest with you.
“At least you can identify with them. Nothing about this United team I like at all. They’re just awful.
“They’re a despondent group of people. Solskjaer is smiling at them they’re that bad.
“United’s away support will never stop singing, but this group of players have drained the energy out of them.”
Solskjaer added: “We haven’t taken enough points, won enough games, scored enough goals and it’s always difficult when you lose your manager halfway through the season.
“It shows us where we are. we’re not living in fantasy land thinking we can catch the top two, 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.”