Neil Warnock and Roberto Mancini woke to newspaper headlines suggesting they were about to be replaced by Nigel Adkins and Michael Laudrup respectively on Sunday.

By the time almost spring-like sunshine had burnt off the early-morning mist such speculation began to seem a bit silly. Or at least it did in Mancini's case because soon after the final whistle Warnock was effectively waving a white flag and accepting he may soon be leaving Leeds United and spending more time driving a tractor at his Cornish home.

Danny Mills, the former Manchester City and Leeds full-back, looked unusually subdued as he interrupted his shift as a radio analyst for some half-time caffeine. Mills had predicted that a Cup exit against Warnock's side would herald the end for Mancini but he had evidently not seen Leeds lose 1-0 at another of Mills' former clubs, Middlesbrough, last Tuesday.

By the end of that defeat on Teesside visiting fans serenaded their manager with chants of "Bye, bye, time to go". A little later, with tension palpable, Warnock, right, was uncharacteristically patronising when asked how much his team were missing Luciano Becchio, the striker sold to Norwich last month.

As two other Argentinian forwards, City's Carlos Tevez and Sergio Agüero, delighted in deconstructing Leeds, one wondered if Warnock – who still maintains Tevez cost him "£1m" in forfeited salary by scoring the goal for West Ham that relegated Sheffield United from the Premier League in 2007 – might carry out his recent threat to "run on and score our goals myself". Even at 64, he might not have done too much worse than El Hadji Diouf and friends at the Etihad but Warnock has since come up with a better idea – a job swap with Mancini.

The only problem he envisages with this little scheme – and what a wonderful slice of reality television it would make – was that Mancini would not be able to cope with life in charge at Elland Road.

Actually, though, one wonders if Mancini's preference for ruling by the fear factor and coming over all authoritarian might prove more effective at a lower level, where the players may be a little more awed by his status as a former star of Serie A.

This was hardly the day to stick pins in the Italian's modus operandi but watching a textbook refereeing performance from Mark Clattenburg and seeing how he cleverly defused festering tensions with quiet words in assorted ears may have given City's manager pause for thought.

Fine a coach as Swansea's Laudrup appears – even if he uses way too much hair gel for a 48-year-old – a touch more Clattenburg-style humanity and humour from Mancini might yet persuade the power-brokers in Abu Dhabi to keep him on after this summer – providing City win the FA Cup, of course.

Possibly Clattenburg's biggest task was dealing with a series of minor aggravations surrounding Michael Brown's first-half indiscretions. The Leeds midfielder tried, and rather comically failed, to intimidate one of the largest examples of what footballers refer to as "Big Units", namely Yaya Touré.

Warnock perhaps realises that Leeds fans – not to mention the club's new Gulf-based owners – are tiring of those scufflers such as Brown he delights in describing as "honest". The former chiropodist also knows that at Scunthorpe and Southampton, Adkins, a former physiotherapist, combined attractive football with Championship success.

The latter's old skills would certainly have come in handy when, in a moment emblematic of Yorkshire struggles, Sam Byram cleared bravely off the line to prevent a City goal, only to be accidentally booted in the face by his fellow defender Lee Peltier.

Leeds's attendant inability to retain possession not only explained both their disappointing mid-table position in an indifferent Championship and the reason why their manager has all but surrendered his job but ensured that well before twilight the heat was, at least temporarily, off Mancini.

Instead, as the fight drained out of Warnock, Mills was left to face down angry City fans hellbent on defending "Roberto". Meanwhile another home supporter inquired how newspaper reporters were going to "spin that into Mancini out", adding sarcastically: "I'm sure you can do it."

It called to mind an old Mark Viduka reply to an interviewer inquiring about the job security of some manager or other. "Aw, man," said the former Leeds striker. "Don't let's get started on regime change."