The Tykes were kicked out of the competition on Wednesday after fielding forward Aiden Marsh in the teams' first-round replay - a game the League One side won 3-0.
Marsh had been on loan at York City when the original tie at Oakwell, a 3-3 draw, took place on November 3 before being recalled by Neill Collins' side three days later.
The Football Association investigated and Barnsley accepted the decision against them, deciding not to appeal, meaning Horsham will travel to League Two's basement side Sutton United this Saturday - only the second time in their history they have reached the second round.
Di Paola had been planning for a Pitching In Premier Division fixture at Hastings that day before discovering his team had received the incredible news this week, with one win now meaning they could draw a Premier League team next.
"It's quite crazy, quite unprecedented," he said.
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