A 1-1 draw away at already-relegated Huddersfield Town means that United's slim chances of finishing in the top four are now over, consigning them to either a fifth or sixth-placed finish with one game remaining.
Solskjaer enjoyed a remarkable start in the Old Trafford dugout after replacing Jose Mourinho on an initial interim basis, but the shock draw in West Yorkshire continues their recent hapless run of just two wins in 10 games.
The Norwegian didn’t hold back in his assessment of his side following the game at The John Smith’s Stadium.
“We are where we are for a reason. Over a long season we haven't been good enough to challenge for the Champions League places,” he told Sky Sports .
"We haven't taken enough points, won enough games, scored enough goals – it’s always difficult when you lose your manager halfway through the season. It's caught up with us a little bit.”
Solskjaer admitted that the Red Devils are a long way behind the title-chasing duo of Liverpool and Manchester City, but qualifying for the Champions League should be a minimum requirement of the club.
The rebuilding job is something he is relishing, though. He added: "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."
United’s draw against the Terriers means that they are the only team to visit The John Smith’s Stadium more than once in the Premier League and not win, having a suffered a 2-1 reverse last season.
"Over 90 minutes we weren't good enough, we missed chances to put the game away, created many chances and didn't let them in our half really,” Solskjaer said.
“When you go to these places, stadiums full of energy, we knew if we gave them hope they'd be up for it and unfortunately we did so.
"Sometimes it happens, concentration, application, confidence drops, it was just strange how we changed our approach to the game instead of playing simple. We chose difficult options.
“It's not come as a surprise but we hoped to show a better performance today."
United end their season next Sunday at home to Cardiff City, whose relegation to the Championship was confirmed this weekend.