Horsham were knocked out following a strong second-half performance by Ryman premier division Bedford Town at Queen Street.
Manager John Maggs said: "Everyone is looking for excuses but there are none.
"We're not good enough at the moment. We need someone to put the ball in the net and I've got to put it right. As soon as we concede a goal we look like a beaten side."
Hornets had the edge during an exciting first half and Ahmet Suleymanoglu forced keeper Ian Brown into a sharp, close-range save after three minutes, then Carlo Castrechino crashed a volley just past the left post five minutes later.
Bedford dominated after the break and took the lead on the hour when Darren Sarrl drilled a low shot into the left corner through a crowded penalty area.
Substitute Daniel French added a second on 83 minutes, stroking an 18-yarder past the helpless Burton, and Eagles got the third six minutes into injury time when Chris Dillon fired home from 18 yards.
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