Timo Werner's first-half goal sealed victory to move fourth-placed Chelsea three points above West Ham in the battle to secure a top-four finish in the Premier League.
While Moyes had no real complaints about the result, he could not hide his dismay at referee Chris Kavanagh's decision to send off Balbuena after a VAR check.
With around 10 minutes left, Balbuena caught Ben Chilwell with his follow-through after a clearance.
It looked to be a natural clash of legs but Kavanagh was instructed by the VAR to check a monitor and he returned to send off the Paraguayan, much to everyone's surprise.
"A rank, rotten decision," Moyes told reporters. "We lost to a team very much in form and maybe we could have got closer without the red card."
Chelsea defender Cesar Azpilicueta escaped a possible handball in his area in the first half and Moyes felt Chelsea's Toni Rudiger could have been sent off for a foul on Vladimir Coufal shortly after Balbuena's dismissal.
"I just thought it was a really poor decision. I don't know who stopped the game. I thought it was supposed to be clear and obvious [error]," Moyes said. "But it shows me the person making the decision has never played the game.
"I don't see anywhere else he can put his foot. Five minutes later the same thing happened with Coufal and Rudiger and if the first was a red why did they not review that incident? The consistency is dire."
While West Ham had a genuine grievance, Chelsea nullified the hosts for most of the derby, again proving what a tough nut to crack they have become since Thomas Tuchel took over from Frank Lampard in January.
Werner's first goal since February always looked like being enough as Chelsea kept a 16th clean sheet in 21 games under the German who had a rather different opinion of the red card.
"The follow-through was a bit dangerous. On TV it looked a bit worse than it actually was. It was a harsh follow-through and they decided it was a reckless and dangerous foul," he said.
"The red card was not a must but it was a decision the referee could take. It was in between, a very hard decision, but maybe not a wrong decision."