The Red Devils were outplayed by Jurgen Klopp’s table-topping side, who cruised to victory at Anfield.
Solskjaer risked a backlash from United fans after the game, however, by insisting the defeat was a step forward.
“For me now, we’ve lost to Liverpool, a team that you all say are fantastic and we’ve been in the game until the last kick of the ball. And, for me, that’s strides forward.
“And of course we’re disappointed losing the game, we don’t want to be behind them in the league.
“But there were signs there that we are on the right track, definitely.”
