Colchester United made eight changes from the side that drew away at Barrow, with Welch-Hayes, Senior and Chilvers the only starters in both.
Luke Norris made his first start of the season after returning from injury, as did Paris Cowan-Hall.
Sammie McLeod made his first start for Colchester United after making his debut ten days ago against Bolton Wanderers at home.
Billy Cracknell and Harvey Sayer were included in the U's matchday squad for the first time.
Colchester United starting XI: George, Welch-Hayes, Sowunmi, Senior, Norris, Cowan-Hall, Chilvers, Scarlett, Kensdale, Gambin, McLeod.
Subs: Coulter, Brown, Poku, Marshall Miranda, Tovide, Cracknell, Sayer.
West Ham U21s Starting XI: Anang, Akinola, Baptiste, Cardoso, Longelo, Coventry, Lewis, Rosa, Chesters, Dju, Afolayan.
Subs: Hegyi, Okotcha, Adarkwa, Appiah Forsan, Sawyer, Ashley, Greenidge.
Colchester United looked to get an early goal and went close on two occasions in the opening minute.
Chilvers, who opened his United account at the weekend had a shot deflected wide before Goncalo Cardoso headed the ball just beyond his own back post.
Luke Norris was back in the starting eleven for Colchester United and looked dagerous up front.
He was unlucky not to get a better shot away in the eleventh minute when he latched onto a Cowan-Hall flick, but Baptiste got back quickly to take the sting out of the shot.
Norris was lurking at the back post ten minutes later when Chilvers lofted the ball into the area, but couldn't quite get his head to the ball.
But it was the Hammers that went closest as the half wore on.
With just over half an hour played, Mesaque Dju had the ball in the top corner of the net, but was offside.
A minute later, Dju struck the inside of the post after a neat through ball, before Welch-Hayes was able to scramble away a clearance.
Shamal George had to be on his guard before half time when the ball broke to Tunji Akinola.
The Hammers' full back had broken free down the right wing, but couldn't beat the onrushing George who saved well.
In the second half the U's domminated the opening exchanges, with Norris going close on a couple of occasions.
But the best chances fell to Ollie Kensdale and Noah Chilvers.
Kensdale was found free from a corner, and scooped the ball over the bar after Senior had picked him out.
And two minutes later Chilvers weaved his way until he was one-on-one with Anang, but the Irons' 'keeper palmed the ball and collected at the second attempt.
The U's were made to pay after an hour played, when West Ham took the lead. Conor Coventry struck the ball into the top corner of the net from outside the area, giving George no chance.
The U's instantly made two changes, replacing Noah Chilvers and Miles Welch-Hayes with Marley Marshall Miranda, and Harvey Sayer who came on for his Colchester United debut.
Jevani Brown was also brought on towards the end of the game to try and fire in an equaliser for the U's.
And Colchester United were close to finding it as the game entered additional time.
First Paris Cowan-Hall had the ball nicked off his head as he looked to power home, but Baptiste just got there first.
Jevani Brown was even closer when he slid in at the front post. The ball was recycled back to the U's sub but he couldn't generate the power to beat Anang.
The full time whistle blew with the U's defeated in their second EFL Trophy Group match, making progression from the competition very difficult.
United still have a home game against Southend in November, but would need favours from the other game to progress.
Next up for Colchester United is the league fixture on Saturday afternoon. Oldham Athletic come to the JobServe Community Stadium as the U's look to make it four without defeat in Sky Bet League Two.