Colchester manager Joe Dunne gave credit to Chelmsford after the non-league side dumped his team out of the FA Cup.
Donovan Simmonds gave the Clarets a two-goal lead after striking either side of half-time and though Michael Rose pulled one back for the npower League One side, Jamie Slabber sealed the giantkilling with a minute to go.
Dunne said: "We're desperately disappointed to lose the match. That's a bit of an understatement.
"I can stand here and say that every ingredient that was needed all seemed to come into play. But I don't want to take anything from Chelmsford - I want them to have a great day and they've earned the right to be in the next round and we haven't.
"That's what the cup is about - it's about earning the right and we just fell short.
"Their first was an opportunistic goal and the second was the same, when we were on top of things in the second half."