Haller scored twice in the space of four first-half minutes and Felipe Anderson added a late third as the Hammers eased into round three.
"Probably the only disappointment is we should have won more comfortably," said boss Moyes.
"But Seb getting a couple of goals will be good for his confidence. We had Michail Antonio scoring for us at the end of last season and now we hope Seb gets on a run of scoring goals."
Haller, who only managed seven goals in his debut season in London, tapped in Andriy Yarmolenko's cut-back before burying Robert Snodgrass' cross with a towering header.
Anderson, who with Haller and Yarmolenko formed a £100million front three against the League One side, rolled in the killer third 10 minutes from time.
But the stand-out player was Josh Cullen, making only his fourth appearance for West Ham having spent the last two seasons on loan with Charlton.
"Josh has done really well," added Moyes. "He's a great boy around the place, he works incredibly hard to improve. I thought he did well tonight.
"We know what we are going to get from Josh. I think he's someone who has put himself in with a chance because we are short of midfield players at times."
Jack Wilshere was conspicuous by his absence from a much-changed squad with the club reportedly wanting to get the injury-prone midfielder off the books.
However, the reason was more predictable, Moyes revealing Wilshere had rolled his ankle in training.
Nevertheless, when asked if the former England international would still be at the club when the transfer window closed, Moyes said: "We'll have to wait and see."
Victory may only temporarily paper over the cracks after West Ham's poor start to the season, a 2-0 home defeat by Newcastle on Saturday, as well as the unrest off the field and the nightmare set of fixtures that awaits them.
But with Arsenal, Wolves, Leicester, Tottenham, Manchester City and Liverpool to come, the League Cup could well be their only chance of racking up some wins before the end of October.
Charlton boss Lee Bowyer, a former West Ham player, said: "In the first half we looked really nervous, we were so afraid of giving the ball away.
"But at half-time I told them to believe you can play, and I thought we were the better side.
"The only thing lacking was that final pass, that final finish. And that's what you pay for."