The National League North Pilgrims tumbled out to Step 4’s Peterborough Sports on Saturday at York Street.
There will be no cup run this year following the 2-0 home defeat to the Southern League Division One Central side.
Elliott refused to bite his tongue after they made front page headlines for all the wrong reason.
“I can’t and I won’t stand up for the players,” Elliott said as Boston exited the competition at the first stage.
“The only description I can offer is that it was totally and absolutely shambolic. We got what we deserved, we were nowhere near good enough.
“I’m embarrassed and so are the players. That was horrendous and it won’t be allowed to happen again.
“I have to say well done to Peterborough Sports, but we didn’t put up a fight or match them in any way.”