But the ball sailed wide of the right-hand upright and if Leicester are to show a profit at the year's end the Pilkington Cup final against Bath on Saturday represents their one remaining opportunity.
Dean Richards sounded a touch forlorn when, looking forward, he said: "You can't have two disappointments in one season." Of course you can. But the losses may not be confined to silverware.
Half a dozen Leicester players are rumoured to be under offer, as it were - property to be disposed of as the game enters the age of professionalism. Both half-backs could be on their way. The Irish stand-off Niall Malone is one of a clutch of four players to have been sounded out by Coventry, while the scrum-half Aadel Kardooni is considering offers from one or two clubs in London, where he now works; Saracens are favourites.
As for Harlequins, they have maintained the hard edge that has emerged this season right to the end. Third place in the League and therefore a shot at European competition next season is just reward for a young, hard-working side.
They were tweaking Tigers' tail from the outset, with their devastating wing Daren O'Leary scoring his 14th try of the season inside two minutes. Leicester clawed their way back but Paul Challinor's two timely drop goals at the end of each half did the trick.
Poor Liley, who passed his own record by scoring 441 points (two more than the mark he set in his first season at Welford Road in 1989-90), had the misery of missing six kicks at goal.
There was one light moment when a hooter was sounded five minutes before the scheduled end of the first half. Referee Ed Morrison blew his whistle and the crowd roared their disapproval. Morrison came off to confer with the official hooter man and then got the confused players to resume.
But that was the only moment of light relief, although there were some seven minutes, late in the game, when it looked as if Quins had rattled the Tigers' cage hard enough to prompt a victorious fightback. Neil Back rounded off a fine driving maul with a 73rd-minute try, the conversion was missed but Tigers were a nose in front. But as the match slid towards overtime Quins battled back upfield, forced a five-yard scrum and from that Challinor pumped over a high drop goal.
Liley's big chance came after three and a half minutes of injury time. But it was a good 45 yards out and a bad moment. Twickenham beckons as a consolation.
Leicester: Tries Liley, Back; Penalties Liley 3. Harlequins: Tries O'Leary, Mensah; Conversion Challinor; Penalty Challinor; Drop goals Challinor 2.
Leicester: J Liley; S Hackney, S Potter, R Robinson, R Underwood; N Malone, A Kardooni; G Rowntree, R Cockerill, D Garforth, M Johnson, M Poole, C Tarbuck, D Richards (capt), N Back.
Harlequins: J Staples (C Wright, 42); D O'Leary, W Greenwood, P Mensah, S Bromley; P Challinor, N Walshe; J Leonard (capt), S Mitchell, A Mullins, A Snow, S Lloyd, G Allison (I Pickup, 40-43), M Watson, R Jenkins.
Referee: E Morrison (Bristol).