Midfielder Joe Cole and defender James Collins were on target at the start of each half for the Irons, with substitute Jabo Ibehre heading in a stoppage-time consolation for the League One side.
It was a fourth straight pre-season win for the Irons, who will now head out to Germany for a training camp and matches against Mainz and Hamburg as preparations step up for the first competitive action at home to newly promoted Cardiff on August 17.
"It was a good workout for us, because Colchester are a couple of weeks ahead of where we are with their season starting earlier, so you would expect we would get a physical game," said Allardyce.
"Our only disappointment was conceding a goal in the last minute.
"The wins, draws or loses mean nothing to what the season will entail, whether you win them all or lose them all, it means nothing to what the first (league) game will be.
"What is the most important thing is that on the 17th of August, everyone is 100 per cent fit, not 90 per cent or 95 per cent, so that they hit the ground running and we can get off to what we hope can be a fabulous start to the season, like we had last year.
"We are looking very good, even at this early stage, so I just hope we can keep it up in Germany."
Allardyce selected a strong squad for the trip up the A12, with summer signing Adrian in goal and veteran Romania defender Razvan Rat in the XI, although England striker Andy Carroll is still not fit from a heel injury.
If all goes well, Allardyce is hopeful the £15million former Liverpool man could be back in action ahead of the first international break.
He said: "Andy is still recovering. He has got four weeks or more to go before he starts full training. His rehab is going pretty well at the moment and will be joining us in Germany, and hopefully he will be available, as will George McCarthy, as quickly as possible
"I hope it will be before (September) for both of them, but being fit and being ready to play are two different things - they may be fit from the injury, but they are unlikely to be capable of playing straight away.
"If we are going to put our lads through six weeks of preparation and then Andy gets fit with two days to go, you would not expect us to play him, would you?"
Allardyce hopes to bring in "at least one more" new arrival before the transfer window closes.
West Ham are considering an appeal for a work permit for Colombian striker Duvan Zapata in a £6.8m deal from Argentinian side Estudiantes.
"It is whether we think we can get the work permit through, that is the problem," said Allardyce, who knocked down suggestions the club were looking at moves for West Brom midfielder Graham Dorrans and Liverpool winger Stewart Downing.
"The fact he is not a full international would mean we have to go to a hearing, and we have to decide if that is worth doing, which we will decide in the next 24 hours, but we would like to (get him) if we could."