David Moyes presided over Sunderland’s latest defeat as a regretful, chastened and surprisingly surprised manager but apparently not one at risk of being fired for suggesting he might slap a female reporter. Islam Slimani and Jamie Vardy scored to extend Leicester City’s winning run but, before that, Moyes’s employers pledged to allow him to continue trying to fight against relegation.

Sunderland declared on Tuesday that their manager’s remarks to the BBC’s Vicki Sparks had been “wholly unacceptable” but that no further action needed to be taken against the Scot, who has apologised both privately and publicly. The club noted in a statement that Moyes had “proactively” informed the club about his comments two weeks ago and said sorry to the reporter.

The Football Association, which has requested Moyes’s observations about the exchange, may decide that stiffer punishment is in order but Sunderland concluded that “the club continues to fully support David in his role as manager”.

Moyes welcomed that statement and said it was nothing less than he expected. He also said he was “surprised in many ways” by the extent of the criticism of his criticism.

The club’s statement was no doubt intended to mitigate any reputational damage caused by what has been interpreted variously as an ill-judged quip or a sinister threat. It certainly did not have the side-effect of inspiring an improvement in Sunderland’s performances on the pitch, most of which have brought derision of another kind this season.

As Moyes and his players trudged away from the King Power Stadium after their latest failed assignment, they might have been struck by the contrast in moods around their club and Leicester.

Nearly six weeks on from the shock firing of Claudio Ranieri, the home of the champions is again at peace, albeit a delightfully noisy and giddy peace. Free beer and cakes were distributed to fans before kick-off to celebrate the birthday of Leicester’s chairman, Vichai Srivaddhanaprabha, while the club’s manager, Craig Shakespeare, has progressed from feeling like a “pantomime villain” in his first press conference after Ranieri’s dismissal to a manager who can do no wrong. This victory brought his record to six wins from six matches. The champions are back in the top half of the Premier League.

Shakespeare had the pleasure of deploying the same lineup that had swatted away Stoke City on Saturday. Moyes, meanwhile, had the pleasure of calling on Lee Cattermole. Injury had kept Sunderland’s captain out of the team since September but here he was cast straight back into the side on a mission to stimulate renewed fight from a team that have seemed resigned to relegation. Sunderland, in fairness, did not lack gusto here. But they were nowhere near good enough to deserve any points.

Neither team shone in a brisk but untidy first half. The visitors hinted at menace from several corners and a couple of long shots but Leicester came closest to scoring.

Jordan Pickford tipped a header by Robert Huth over the bar after a free‑kick by Riyad Mahrez. The goalkeeper excelled just before the break when he dived across goal to turn away a curling 20-yard shot by Demarai Gray.

Gray posed a regular threat. It hardly came as a surprise even to Moyes when Cattermole was booked for trying to sabotage a Leicester break by tripping the young winger in the 34th minute.

Moyes saw no need to change approach at half-time, hopeful that his team could eke out a goal even if their top scorer, Jermain Defoe, had barely been involved in the first half.

Sunderland fans sensed an opportunity in the 54th minute when Sebastian Larsson lined up a free-kick at the edge of the Leicester box. Larsson disabused them of their optimism by nearly hitting them with his shot. Three minutes later another free-kick by Larsson led to Defoe’s first shot of the night. He struck it crisply but straight at Kasper Schmeichel.

Shakespeare was concerned. Just after the hour he made a double substitution, introducing Slimani and Marc Albrighton. Soon that pair combined to open the scoring. Albrighton crossed from the left and Slimani outmanoeuvred the hitherto solid Lamine Koné before heading into the net from seven yards. Shakespeare’s changes had paid off.

Moyes hoped to have a similar impact when he, too, made a double substitution in the 72nd minute, throwing on Wahbi Khazri and Victor Anichebe. The latter almost granted his manager’s wish but his shot from 15 yards was deflected on to a post. Then Vardy deepened Moyes’s misery. After more excellent work by Albrighton and more sloppy defending by Sunderland, Vardy walloped a shot into the net from 16 yards.

“I thought we’d done a really good job up to 60 or 65 minutes but ultimately we allowed a cheap cross into the box and we should have won the header for the first goal,” said Moyes, who said a second defeat in four days left his team needing an improbable feat to avoid relegation. “We needed to win one of these two away games. What I didn’t put down was a win against a Manchester United or an Arsenal or a Chelsea in my remaining fixtures. I now have to win at least one of those.”