The U's, who have now lost their last seven games, made a disastrous start when defender Mark Connolly gave Crawley a fourth-minute lead and late strikes by Billy Clarke and Nicky Adams gave the Red Devils their first victory in four games.
Dunne said: "We let in sloppy goals and it's been systematic over the season.
"It was a bad defeat, but it was not a 3-0 game. Unfortunately we have started the year how we ended it and it was not what we wanted."
Colchester have only scored three goals during their losing run while conceding 18 and Dunne believes that some of the problems that are being created are "avoidable".
He added: "We have got to start better and we worked at it all week. Having said that, after 10 minutes, we controlled the rest of the first half, but things are not breaking for us at the moment.
"We need to keep pushing. We did a lot of good things and over the course of the transfer window we will try to bring in a couple of players. We need to do it."