Burnley triumphed at Old Trafford on Wednesday for the first time since 1962, with Chris Wood and Jay Rodriguez scoring in a 2-0 win.
United have now lost more Premier League games than they have won since Solskjaer’s permanent appointment in March and are 30 points behind leaders Liverpool, who also have two games in hand on their rivals.
The Norwegian boss reportedly retains the backing of the United hierarchy despite the club’s dismal run, but Wales winger James knows they must improve quickly.
“Obviously disappointing,” James said following the defeat. “Today obviously wasn’t good enough. We know that and obviously the fans know that as well.
“We need to, as a team, take chances better. Today we had quite a number of shots.”
James bemoaned a lack of cutting edge during a promising United start that quickly unravelled, with Solskjaer’s side mustering little response to Burnley’s goals either side of half-time.
Rodriguez’s stunner early in the second half led to renewed, furious chants calling for owners the Glazers and executive vice-chairman Ed Woodward to leave, with thousands of fans rising to their feet as “Stand up if you hate Glazers” echoed around the ground.
There were jeers at the final whistle but there was still support for Solskjaer and the players between songs aimed at the club hierarchy.
“I think every week, home and away, they cheer us on and stick by us,” said James. “We’re obviously going to react to this. We know that wasn’t good enough today.”
United have a frantic fixture schedule coming up, with an FA Cup fourth-round tie against Tranmere or Watford on Sunday.
A trip to Manchester City for the second leg of the League Cup semi-final, a match they head into 3-1 down, follows on Wednesday before attention turns to narrowing the gap to the top four, with United still fifth.
“I think that’s obviously still up for grabs,” James said of the Champions League spots. “We’ve got to keep fighting.
“We’ll reflect on this game and then see what obviously went wrong today. Then we’ve got two big cup games coming up. We’ve got to go into that with heads held high.”
