Following over Morton and Partick Thistle in recent weeks, Accies were minutes away from another impressive result after Jonathan Page had headed them into the lead with his first-ever goal for the club.
The pressure from the home side proved too much for Reid's men, though, as teenagers Conor McGrandles and Lewis Small netted in the closing stages to deny Hamilton a third successive win.
The Accies have gone back to basics in a bid to strengthen their young outfit in recent weeks, but they remain eighth in the league after the cruel finale at Falkirk.
Reid said: "We never played really, but we scored from a set-piece and we were eight minutes away from taking another three points, which would have been a tremendous result for us.
"But, we can't complain. They have had enough possession and enough crosses into the box.
"We had two smashing wins on the bounce and this is a wee setback for us."