Rovers, flying high in the Wessex Premier, were stunned 3-1 at home by lower division Andover Town in a first qualifying round tie.
Josh Petrie took his seasonal tally to 11 with a brace in one of the most surprising results of the round.
‘That was one of the worst performances I’ve seen here,’ said Wilkinson.
‘We had six key players missing but we should still be performing better than that. We went out with a whimper - we hardly had a shot in the second half.
‘I would like to apologise to the paying customers, the chairman and the committee. It’s a cup we wanted to have a good run in but collectively - myself included - we just weren’t good enough.
‘I didn’t think they (Andover) were that good, but we made them look like world beaters.
‘It’s a bit of a wake-up call. I have players knocking on my door asking why they’re not playing. Here they get an opportunity, at home, in the sunshine … they’ve made my job a bit easier in terms of bringing the six who were missing back in.’
Baffins were missing skipper James Cowen, top scorer Tommy Scutt, Charlie Williamson - ‘probably our best player so far this season’ - Alex Przespolewski, Fuzz Kanjanda and Josh Warren against Andover through injury, illness or unavailability.
Among the players recalled to the starting XI was midfielder Harry Sargeant, who a few months earlier had been part of the US Portsmouth squad that had come within a penalty shoot-out of the 2021/22 Vase final.
Short of numbers, Wilkinson brought on two 16-year-olds in the second half - striker Liam Brewer and midfielder Harvey Welham.
‘The fact two 16-year-olds were our best players says it all,’ the boss remarked. ‘They were a credit to themselves and their families.
‘I said to the players after they need to buck themselves up - those lads are close to taking some of your places. I don’t care if they’re 16 - if they’re good enough, they’re old enough.’
Centre half Ed Sanders netted a first half equaliser, but Andover restored their lead just before half-time and added a third in the second half.
Baffins return to action on Wednesday against two tiers higher Hartley Wintney in the Hampshire Senior Cup at the PMC Stadium.
Hartley will also be aiming to bounce back from a bad loss - in their case a 6-1 hammering at Southern League Premier South table-toppers Hayes & Yeading.