Ruben Amorim welcomed a rare clean sheet in Manchester United's 1-0 win at Fulham on Sunday but did not gloss over his side's need to improve despite a vital three points.
Lisandro Martinez's deflected winner offered some respite to Amorim, who has won just four of his 12 Premier League games in charge.
United climb to 12th in the table, now a comfortable 13 points above the bottom three.
But their performance was in keeping with many others under two different managers this season, against sides with a fraction of their budget.
There was little to get United co-owner Jim Ratcliffe excited as he watched on in west London, but victory does dispel any remaining notion that United could be dragged into a relegation battle.
"Not a great game and you can feel it, no great chances," said Amorim
"We tried to control the game, tried to play our game but we need to improve a lot with the ball.
"It's really important (to keep a clean sheet) because clearly you are closer to wining games and getting confidence. We didn't suffer too much today and that's a good sign. It's not just the clean sheet, it's the way we defended."
Fulham made the brighter start but were also guilty of a lack of penetration in a pedestrian 90 minutes.
Andre Onana returned in goal for the visitors despite his error for Brighton's third goal in the Seagulls 3-1 win at Old Trafford last weekend.
The Cameroonian was forced into two early saves from the lively Alex Iwobi.
It took just before the hour mark for United to seriously threaten when Bruno Fernandes' clever free-kick slid under the Fulham wall but just the wrong side of the post.
Rasmus Hojlund's return had been one of five changes made by Amorim from a dramatic 2-1 Europa League win over Rangers on Thursday.
But the Dane's goal drought extended to 11 games as he barely posed a threat before being replaced by Joshua Zirkzee.
And it was little surprise that it was a moment of fortune rather than inspiration that broke the deadlock.
Martinez took aim from long range but in his desperation to block, Sasa Lukic's deflection saw the ball fly over goalkeeper Bernd Leno and dip into the top corner.
"I think it was lucky, but an important win," said Martinez.
"It means a lot. Not only to the fans, but for us because we have suffered a lot."
Fulham should still have snatched a point as United's frailty from set-pieces was exposed.
Joachim Andersen was afforded a free header from a corner but Toby Collyer got back to head off the line.
The visitors could also have extended their advantage deep into stoppage time when Amad Diallo's strike was ruled out for offside by a VAR review.
Defeat dampens Fulham's European ambitions as they remain in 10th, seven points off the top six.