"We simply hammered them - yeah, we hammered the Hammers," he said, laughing at his own joke. As they trudged off to board their coach back to London, the visitors did not share Kelly's sense of humour.
For Harry Redknapp's team, beaten by a rag-bag assortment of seasoned veterans and lower-division journeymen, shown up in their application by a club battling debts of pounds 7m, it had been another in their long succession of away-day disappointments at lesser clubs in the FA Cup.
A single first-half goal, struck with perfect timing on the volley with his left foot by former Oldham Athletic and Sheffield United stalwart Nick Henry, settled the outcome, but hardly did justice to Tranmere's superiority on an afternoon when the grey streets of the Wirral touched and melted into the grey sky overhead.
The home side were simply more focused and organised than their Premiership counterparts, and the contrast in commitment shown by both teams made a mockery of their respective league positions.
"They just didn't perform on the day," Kelly said. "It wasn't a good day for them, but it was a great day for us. I feel for them because it is a club I have a soft spot for. I always look for their result first every week, but there's no doubt that we deserved to win.
"We have been playing like that for the last five or six weeks. In all honesty, we didn't let them get started, never mind settle down. We knew how they would play and we prepared all week on how to stop them finding their pattern."
Perhaps wary of Tranmere's well-disciplined offside trap, Redknapp tried to change his system, with a flat-back four and a diamond formation in midfield. This allowed the toothless Paulo Di Canio to drift wide to feed Trevor Sinclair in attack. But it was all too easy for the home side.
Redknapp was forced to beef up his attack with the half-time introduction of Paul Kitson. The lanky Wanchope followed later, replacing the disappointing Di Canio who was restricted to arguments with the crowd, disagreements with rival players and at one stage, an arm-waving row with his own bench when he and Sinclair had been halted for the umpteenth time by a raised flag.
"The Italian didn't perform for us," Redknapp acknowledged. "For whatever reason he had his first bad day and we couldn't compete. This sort of thing has been happening to us for years and it's all so disappointing."
West Ham's best opportunity was thwarted by the highly rated goalkeeper Joe Murphy after 37 minutes. He kept out Frank Lampard's close-range header from Sinclair's cross before Neil Ruddock wasted the rebound in front of a gaping goal. Redknapp could only watch in despair.
For his opposite number, John Aldridge, it was just reward for a wholehearted display from a side that almost went out of business in the summer. Yet another FA Cup triumph for a man with a fine association with the Twin Towers of Wembley.
Goals: Henry (21) 1-0.
Tranmere Rovers (4-4-2): Murphy; Morgan, Hazell, Challinor, Roberts; Parkinson, G Jones, Henry, Mahon; Allison, Kelly (Taylor, 88). Substitutes not used: Black, Koumas, Frail, Achterberg (gk).
West Ham United (4-4-2): Hislop; Potts (Kitson, 46), Ruddock, Ferdinand, Minto; Lampard, Foe, Cole, Lomas; Sinclair, Di Canio (Wanchope, 74). Substitutes not used: Keller, Byrne, Forrest (gk).
Referee: D Gallagher (Banbury)
Bookings: West Ham: Sinclair.
Man of the match: Allison.
Attendance: 13,629.Reuse content