Bruno Fernandes warned his Man United teammates they will only compete for trophies this year by ensuring results are seen out more than they have been so far this season.
United led 1-0 at the break thanks to a first half goal from Anthony Martial, the assist for which was laid on by Fernandes himself.
But Everton came out fighting in the second half and grabbed a deserved equaliser through Andros Townsend after a quick counter attack put the Englishman through one-on-one with David de Gea.
It was the second game in succession United failed to pick up all three points, after their shock defeat on home soil to Aston Villa last weekend.
Fernandes missed a penalty in that fixture, but has urged his colleagues they need to shape up to challenge for major honours.
"We should have more points," Fernandes vented to BBC Sport after the game. "We drop points at home and we should not do that.
"If we want silverware at the end of the season, we have to do much better."
United have also been held to a draw by Southampton this season, and were fortunate to leave the London Stadium with all three points after Mark Noble's late penalty was saved by David de Gea.
On the whole, United have so far looked vulnerable defensively and over reliant on singular match-winning moments from key players.
Fernandes has those in abundance, as his assist saw him record a 50th goal contribution in just 58 Premier League appearances since joining United (via Opta Joe).
Sadly, his compatriot Cristiano Ronaldo could not provide one of his own against Everton, despite his midweek heroics in the last-gasp win over Villarreal.
Ronaldo actually started on the bench as Ole Gunnar Solskjaer opted to give the superstar a rest and afford chances to Martial and Edinson Cavani in attack.
But the Portuguese forward was left ultimately frustrated after coming on as a 57-minute substitute, shortly before Townsend levelled the scoring.
The breakaway goal Prompted Ronaldo to berate his teammates for not cutting out the attack sooner, and he stormed down the tunnel at the final whistle.
Rio Ferdinand was in agreement with Fernandes after the match, urging his old team to again make Old Trafford an imposing place to visit.
"They dominated the ball but at the same time they had 13 shots to Everton’s 12 so it’s not like they kept them under the cosh," Ferdinand told BT Sport.
"They’ve got to get out of this, they’ve got to create a fortress here, create a place people fear and at the moment, teams come and build confidence through a game and that can’t be right."
Solskjaer felt his team controlled proceedings but accepted his side were too susceptible to counter attacks and highlighted a "key lesson" for his side.
"We didn’t concede many chances today but we conceded a goal so we had to deal with a couple of moments, we didn’t, they break and counter attack and outmuscled so we should’ve cleared it but that's in every game in the Premier League, you can work everyday on system and defending but it has to be dealt with there and then.
"We gave them a few counter attacks, I don’t know the stats but I know we had the ball most of the time, they didn’t play through us at all really. They counter-attacked that was the same Wednesday night [vs Villarreal]."
He added: "We have to be better when to risk it how not to be counter-attacked that’s a key lesson today because they do create big chances from quick breaks.
"We weren't too open, we had enough players behind the ball but we didn’t deal with the ball, the tackles when we should have, good goal by them but when they counter from one side the goal is going to happen from the other side so we just didn’t regroup and reorganise well enough."
