Brian Wilson's first goal since November 2010 put the League One U's, who were reduced to 10 men in the second half when Magnus Okuonghae was sent off, on course for their first win in the competition for nearly five years.
But goals from former Colchester winger Medy Elito as well as Brian Saah, Abu Ogogo and Louis Dennis, made sure League Two Dagenham triumphed.
"The boys will take a lot of confidence from that," Currie said. "They will have seen what they're capable of.
"The first half went pretty much as expected. Colchester are a good passing team and they played very well in the first half.
"But the gaffer (Wayne Burnett) reiterated a few things at half-time - and it was a fantastic response from us."
Currie added: "The game changed when he (Okuonghae) got sent off. He's a big player for them, a big powerful player at the back.
"Sending-offs always have a big impact on the outcome of games and we know that.
"But it was nice and positive to see that, even when they had 11 men we were more likely of getting back into the game.
"When they went down to 10 men, well then I thought we were very dominant."