Fallon saw Swansea City triumph 2-1 at the Glass World stadium thanks to first half goals from Gorka Pintado and Guillem Bauza – a result that sees them travel to the South Coast to take on holders Portsmouth in the next round.
But he was nowhere near downbeat by his side’s performance and indeed looked back over some good chances that went begging when he spoke to BBC Sport after the game.
“We had three or four good chances in the first half and might have taken them.
“When they come along in games like these you’ve got to take them. Swansea had a lot of quality about them, and their finishing was very good.
“But it’s a credit to the lads that they are disappointed to have lost to a Championship team.
“Now comes the hard part of picking the players up when all the publicity ends.”
Histon’e attentions now turn back to the Conference and their drive to win promotion to the football league.