Newly-installed Tony Smith saw his side fight hard against champions Wigan Warriors and show improvement in a number of areas.
However, at the end of it all, the East Yorkshire club - who sacked Tim Sheens on Wednesday - were undone by Sam Powell’s 79th minute drop goal, a “miracle play” from 45m out.
It was a cruel way to fall given Rovers had fought back from 14-6 down at the interval to lead 18-14 following excellent tries from Will Dagger and Ryan Lannon at the start of the second period.
Even when the visitors - who have had their own struggles losing their last three games - went ahead, KR still had chance to at least level only to painfully miss out.
Josh Drinkwater’s 40m drop-goal attempt, with just three seconds remaining, was pulled wide and, therefore, his side were not even left with the chance to fight it out again in Golden Point extra-time.
It was yet another winning position that deserted them, summing up some of the issues that had led to Sheens’ demise.
Furthermore, they thought they had already scored a potentially match-winning score when Chris Atkin touched down in the 71st minute.
Josh Drinkwater’s high kick came loose following Craig Hall’s challenge but referee Scott Mikalauskas ruled Hall knocked it forward.
Those who saw replays - there was no video referee - said otherwise.
To make matters worse, bottom-placed London Broncos produced a stunning and shock 23-22 win over leaders St Helens which means Rovers only stay off the foot of the table due to a superior points difference.
The two sides meet in Ealing on Thursday week which is already looking like a hugely significant contest.
By that time, the former Leeds Rhinos and England coach Smith will have had some time to actually work with his new team; yesterday’s Captain’s Run was his only session with them before today’s game and even that came at a cost.
Danny McGuire, the veteran playmaker who had helped win his first Grand Final with Leeds in 2004, strained a calf which kept him out of the side and saw Dagger recalled for his first game since Easter Monday.
Rovers lost Danny Addy to a hamstring injury as early as the 18th minute and also saw Kane Linnett, the Australian centre, stretchered off following a sickening head knock just before the hour.
Credit Wigan, though, as they had their own strife in the department, Wales prop Ben Flower limping off with a back injury in the tenth minute and their ex-England full-back Zak Hardaker not returning for the second period.
Furthermore, George Williams, the England stand-off, missed all three of his admittedly difficult touchline conversions so it could be argued Rovers should never have really got so close.
That will not help them this morning. Smith knows his main priority; with the worst defence in Super League, the Robins simply must stiffen up if they are to avoid being dragged further into that relegation dogfight.
Wherever he has been, the 52-year-old has always improved sides and, with a dozen games left to go - starting with Warrington Wolves on Saturday who he left 18 months ago after nine years - this will be a challenge he will relish.
Rovers quickly turned around that half-time deficit at the start of the second period.
Joel Tomkins’ instant tip pass back inside to Hall saw the full-back surge through and Dagger supported up the middle.
Next, two superb flick passes from Joel Tomkins and Jimmy Keinhorst saw Ben Crooks escape, before Drinkwater’s dart continued at the next play and prop Lannon held off tacklers to stretch over on the last tackle for his first try in Rovers’ colours.
Ryan Shaw made it 18-14 but some poor defence on their left saw Liam Marshall level in the 65th minute.
They had been competitive throughout but conceded two tries inside five minutes just before the interval to change the context of the game.
The excellent Dan Sarginson cruised in following a slick right-edge move after Liam Farrell had initially made ground down the left, punching through Jimmy Keinhorst’s attempted tackle.
Joe Burgess then scored with the final play of the half following some fine handling from forwards Morgan Smithies and Taulima Tautai on halfway put George Williams in motion.
Fortunately, for KR, Williams - who had taken over kicking duties from the struggling Hardaker - missed both conversion attempts.
England stand-off Williams had scored the opening try of the afternoon, Hardaker improving, on 11 minutes although there was some good fortunate about that, Burgess’ pass after being sent clear by Oliver Gildart clearly forward.
Rovers did have pressure but failed to do much with it, meaning they were grateful of Keinhorst when he intercepted Liam Farrell’s offload and managed to go 80m to score.
Shaw made it 6-6 but then came those crucial defensive lapses and agony at the end.
Hull KR: Hall; Crooks, Keinhorst, Linnett, Shaw; Drinkwater, Dagger; Harrison, Addy, Masoe, Tomkins, Hauraki, Lawler. Substitutes: Atkin, Maria, Lannon, Mulhern.
Wigan Warriors: Hardaker; Marshall, Sarginson, Gildart, Burgess; Williams, Leuluai; Flower, Powell, Clubb, Isa, Farrell, O'Loughlin. Substitutes: Bullock, Sharrocks, Smithies, Tautai.
Referee: Scott Mikalauskas (Leigh)