A first home defeat to Wolves in 42 years leaves United still seventh in the Premier League table, four points adrift of the top four.
But it was another lacklustre performance that was just as concerning as the result for Rangnick as the Red Devils were thoroughly outplayed.
“We didn’t play well at all, neither individually or collectively,” said Rangnick, who had taken 10 points from his first four games in charge.
“We didn’t press at all. We tried but after 10 or 15 minutes we were not able to get into those pressing situations.
“The games show we still have a lot of work to do. Especially against the ball, but also in the first half when we had the ball, we had too many unforced giveaways.”
United leftback Luke Shaw questioned the team’s commitment after the defeat saying, “We look at our squad, our team, the players we have, we have unbelievable quality. Sometimes quality isn’t enough.
“We need to bring the intensity, we need to bring being more aggressive and we need to bring more motivation. I think maybe from the outside today, it didn’t look like we had any of them three.
“Inside the dressing room we know we want to win, we know what we want but I think when we step out on that pitch we need to give 100%, everything we’ve got.
“I think to win these types of games against a tough team like Wolves we all need to be 100% committed because we know it’s always close games whoever they play.
“We have time now to refocus. We’ve got a long training week and maybe the manager can bring some more ideas on what he wants on the pitch.”
An injury crisis at centre-back with captain Harry Maguire, Victor Lindelof and Eric Bailly all missing, forced Rangnick to hand Phil Jones his first Premier League appearance in two years.
But the former England international was one of few United players to emerge with any credit from a ragged display that raises questions over their chances of qualifying for next season’s Champions League.
Cristiano Ronaldo was named United captain for just the second time in the absence of Maguire.
In his new year message on social media, Ronaldo said he was “not happy” with the state of affairs at United and that “we have to work harder, play better and deliver way more than we are delivering right now.”
However, there was no sign of improvement as Ronaldo was kept quiet up against a number of his Portuguese international teammates.
David De Gea was the difference between the sides when United won 1-0 at Molineux in August and the Spaniard was again his side’s saviour with a finger tip save to turn Ruben Neves’ volley over early on.
Wolves managed more shots in the first half than they had in their previous three matches combined.
But Bruno Lage’s men have scored just 14 goals in 19 league games and again failed to make their control of the game show in the scoreline.
“It is one more victory,” said Lage. “Lovely stadium, a place with a lot of history, but the most important thing is how we played.
“We played in our way, we controlled the first half and missed a lot of chances. We win three points but again we have more chances than goals.”
Rangnick left Bruno Fernandes on the bench after the Portugal midfielder missed Thursday’s 3-1 win over Burnley due to suspension.
However, it was not until his introduction on the hour mark that the home side even began to threaten a breakthrough.
Fernandes should have opened the scoring when he rattled the crossbar with the best chance of the match from Nemanja Matic’s cross 23 minutes from time.
Moments later his free-kick was headed home by Ronaldo, but clearly from an offside position.
United’s attacking flurry quickly fizzled out and Romain Saiss hit the bar from a free-kick as Wolves continued to pose a threat.
The visitors finally got their reward eight minutes from time when Jones’ header fell kindly for Moutinho at the edge of the box and he drilled low into the bottom corner.
Jose Sa was still needed to make a vital save from another fierce Fernandes free-kick with virtually the last kick of the game.
Victory lifts Wolves up to eighth, just three points behind United.