Having recovered from their recent FA Cup exit by beating Everton and Nottingham Forest, Wimbledon do indeed deserve credit. They had the best of this occasionally rousing draw, and would have won had Ludek Miklosko not been at the top of his game in the West Ham goal.
Kinnear's jocular reaction to the question of whether his side would stay up gave way, thankfully, to a more reasoned analysis. He accepts that one more win would ensure safety for his side. "I don't think any of the lower sides are going to get past 37 points," he said.
He was understandably pleased with his team's response to going a goal down after just six minutes. Vinnie Jones, whose miskick had conceded the corner from which Julian Dicks headed West Ham into the lead, made amends just four minutes later with an equaliser which deflected in off Danny Williamson.
In previous years, West Ham might have fallen apart in such circumstances, and Wimbledon certainly piled forward as of old, throwing four men forward and backing up like mad. But there is a solidity about the East Londoners now which has enabled them to rise to mid-table security in the last two months and augurs well for next season.
Slaven Bilic, their recently acquired Croatian international, has already formed an urgent defensive partnership with that other foreign import, Marc Rieper, in West Ham's traditional soft centre. The full-back positions, too, are formidably manned - Tim Breacker, back from injury, repulsed one challenge from Jones like a bear shrugging off one of its cubs, while Dicks appears to have purged much of the mindless aggression from his game without diminishing its positive impact.
Up front, however, West Ham were far less convincing. In the absence of the injured Tony Cottee, the dainty Portuguese signing Dani proved about as useful as Bambi, save for one speculative first-half shot which passed narrowly wide of the post.
The problem for West Ham, was that, for them, this match did not matter. Their hard work this season has been completed.
Goals: Dicks (6) 1-0; Jones (10) 1-1.
West Ham United: (4-4-2): Miklosko; Breacker, Rieper, Bilic, Dicks; Hughes, Williamson, Bishop, Rowland (Slater, 63); Dani, Dowie. Substitutes not used: Martin, Sealy (gk).
Wimbledon: (4-2-4): Sullivan; Ardley, Perry, Blackwell, Kimble; Jones, Earle; Gayle (Goodman, 69), Holdsworth, Ekoku, Clarke (Castledine, 80). Substitute not used: Thorn.
Referee: P Durkin (Portland, Dorset).
Bookings: West Ham: Bilic. Wimbledon: Jones.
Man of the match: Miklosko.
Attendance: 20,402.Reuse content