It is becoming a dire festive period for José Mourinho. This draw with Burnley, following the identical result at Leicester City on Saturday, means Manchester United will trail Manchester City by 15 points should Pep Guardiola’s men beat Newcastle United on Wednesday night.

If it is not already, the deficit to United’s great rivals will soon be embarrassing. Given Mourinho’s personal history with Guardiola these are uncomfortable times for the Portuguese and the delirious visiting support signalled so, at one point comparing him unflatteringly with the Catalan.

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As United spent virtually all of the second period camped in Burnley’s half, Mourinho could not fault the effort. The problem is more fundamental: a lack of quality where it counts most, in front of goal. Still, having trailed 2-0 at the break, the comeback to share the points showed spirit, an element their manager hailed.

“At half-time I need my players to believe in me and accept the risk, not to be afraid to lose three or four, not to be afraid of a possible negative reaction from the supporters,” Mourinho said. “And I’m very happy with their character. Apart from that, also the way they played, they tried to break a very organised wall, I keep saying that to defend well is a quality and they defended very well, so also credit for them to concede only two goals.”

After the “childish decisions” bewailed by Mourinho for allowing Leicester to sneak a late equaliser, he made four changes. Victor Lindelof and Jesse Lingard dropped to the bench and Anthony Martial and the injured Chris Smalling were not in the 18. Marcus Rashford, Marcos Rojo, Luke Shaw and Zlatan Ibrahimovic were drafted in, with the Swede making a first Premier League start this season.

Sean Dyche’s only change from the 3-0 home defeat by Tottenham Hotspur was Ashley Barnes for Chris Wood, who has a knee problem. Burnley started in excellent fashion. Jeff Hendrick forced Rojo into conceding a free-kick down the left and when Johann Berg Gudmundsson swung the ball in a poor defensive header from Romelu Lukaku allowed Barnes to fire Burnley ahead after three minutes.

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After Mourinho’s latest moan about the schedule in the programme his mood will have darkened further. United’s profligacy cost them at Leicester and they were culpable again in their next attack here. Ibrahimovic’s cross fell precisely for Juan Mata to head but he connected only lightly as Nick Pope’s goal gaped.

Burnley were proving sharper. When the ball was moved to Gudmundsson down his right corridor the Iceland international was allowed copious time to send in a ball that fell straight on to Scott Arfield’s boot and, though he beat David de Gea, the ball struck the bar.

At the other end, Shaw warmed Pope’s fingers with a 25-yard effort and this followed an Ashley Young cross from which Lukaku went close with a header. Then a slick move involving Shaw, Rashford, Ibrahimovic and Mata took United swiftly into the area before Burnley snuffed out the danger by conceding a corner. A second followed quickly but Shaw’s delivery was cleared with ease. Back came United via a strong Young run along the right. He fed Lukaku yet when the centre-forward beat two defenders and stood the cross up, Ibrahimovic’s attempted bicycle kick put off an in-rushing Rashford.

When Burnley next pushed forward they showed United how to finish. Arfield was clattered by Young and from the resulting free-kick 25 yards out in a central position Steven Defour curled the ball beyond De Gea into the top-right corner to double Burnley’s lead.

Ben Mee remained focused enough to prevent United pulling one back moments later. Rashford stole half a yard but his shot was cleared from the goalline by the visiting captain. As the half petered out a quiet Paul Pogba fired an attempt wide, epitomising United’s afternoon.

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Mourinho made a double substitution for the second half, with Ibrahimovic and Rojo taken off for Lingard and Henrikh Mkhitaryan. Nemanja Matic dropped into Rojo’s centre-back berth, with Lingard and Mkhitaryan operating in midfield in a 4‑1‑4‑1 formation. There was nearly an instant dividend. Young fired in a low cross from the right and Lingard made contact but the effort was deflected on to the bar by a Pope hand. Soon, though, Old Trafford did roar as United found the net. In a near identical move, Young zipped in a cross and this time Lingard scored with a back-heel to the crowd’s delight.

United’s tempo quickened but their hopes of scoring twice more to win the game looked slim against a parsimonious Burnley defence. Mourinho’s men kept possession without really posing a threat to Pope’s goal. A Rashford free-kick from the left that cleared everyone and went straight out was symptomatic. But, with defeat looming, Lingard struck in the first minute of stoppage time to secure a point.

It left Dyche content, though. “To come here and get a point is very pleasing,” he said. “It was tough. That was why they have only lost once here this season. You have to remind yourself of them facts. You have to look at the people they brought off the bench.”

Burnley finished with seven yellow cards, which means a Football Association charge. But Dyche will hardly care.