A lap of appreciation has rarely seemed more appropriate at Goodison Park. Everton ended their home campaign with another solid win and a lap of the pitch to say thanks to supporters for remaining united throughout a season of unprecedented challenges. Sean Dyche, players and fans alike all deserved their communal moment in the sun.

Everton signed off at Goodison with a fifth consecutive home win and clean sheet, equalling the club’s Premier League record, courtesy of Abdoulaye Doucouré’s header against relegated Sheffield United. Only Manchester City and Arsenal have collected more points since the beginning of April than Everton, who would be 11th in the table but for the two separate points deductions that could have derailed lesser teams and managers. “It was nice to have that moment,” said Dyche of the end-of-season tradition. “The players have put a real shift in this season, as have myself and the staff, and the fans have paid us back.”

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It was a rare carefree afternoon for Everton. On the surface at least. The sun shone, fingernails went unchewed with Premier League survival secured before the final home game for the first time in three seasons, and Dyche’s team were for the most part comfortably superior. But, of course, Everton’s existence is anything but carefree.

In the programme Kevin Thelwell, Everton’s director of football, echoed the manager’s warning that they will have to raise money this summer due to the club’s dire financial situation and uncertainty over a takeover. “We cannot lose sight of our central objective to protect the long-term stability of the club,” wrote Thelwell. “That does mean players will be sold, and also that every tool at our disposal will be used to secure new additions to the squad, including utilisation of the loan market.”

Another day brought another round of negative stories involving 777 Partners, the troubled investment firm that Farhad Moshiri and seemingly Farhad Moshiri alone considers “the right people” to take over Everton. The company is reported to have called in bankruptcy specialists and removed co-founders Josh Wander and Steve Pasko from the board of its football division. And their proposed takeover is still not officially dead.

Everton’s players and management, to their immense credit, continued to perform as though immune to serious distractions, whether they be points deductions, the threat of administration or the doubts over their own futures.

Dominic Calvert-Lewin dominated United’s back three almost single-handedly. The striker, first to almost every ball in the air and on the ground, created an excellent early chance for Doucouré to open the scoring when bringing down James Tarkowski’s long pass and nutmegging Auston Trusty. Doucouré should have scored but shot straight at goalkeeper Wes Foderingham.

The Everton pair combined again when giving Dyche’s side a deserved lead. Dwight McNeil released Calvert-Lewin with a perfectly weighted pass and, as Foderingham raced off his line, the forward glided around the United keeper and clipped a cross back from the by-line. This time Doucouré made no mistake with a close-range header. The goalscorer had been reprimanded by Dyche moments earlier for not sticking close enough to Calvert-Lewin to capitalise on his intelligent touches. Smart advice.

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United’s cause could have been further undermined moments later when Jack Robinson pushed Calvert-Lewin to the ground with both hands raised and some force. The United captain completely lost his head but was shown only a yellow card by referee Stuart Attwell. Calvert-Lewin was also booked, perhaps for something he said, to widespread disbelief. “The modern rule is he is probably going to walk,” said Dyche. Chris Wilder countered: “I know some people will think it could have been more but I’m glad the referee and VAR made a sensible decision.”

The visitors improved after the interval and repeatedly stretched the Everton defence without finding the end product their approach demanded. Ben Brereton Díaz, Cameron Archer and Gustavo Hamer all put decent chances wide while Jarrad Branthwaite, quite possibly appearing for Everton at Goodison for the final time given he represents the club’s most saleable asset, almost caught out Pickford with a risky backpass.

“We had chances but ultimately we haven’t got enough quality to get back in the game,” Wilder admitted. “That has been the case from game one to game 37.”