The visitors looked set to secure a point after Tim Howard produced a string of saves on his return from injury to frustrate the Premier League leaders on Wednesday.
Chelsea were not to be denied, though, as Willian's deflected strike a minute from time ensured Jose Mourinho's side remain seven points clear at the top of the table.
Willian's winner came just after Barry had been shown a second yellow card for a challenge on Chelsea's match-winning Brazil international, which resulted in a mass confrontation.
Everton boss Martinez accused Chelsea's players of influencing Moss and felt Barry's dismissal was a turning point.
He told BBC Sport: "Every time a player loses a challenge it feels like the weight of the world is on the referee's shoulders and he feels he needs to react. To give Gareth Barry a second yellow card because of the reaction from Chelsea's players is disappointing.
"They surrounded the referee and their conduct was a real shame. It created a little bit of belief for Chelsea and the goal came as a consequence of that. It was a very scrappy goal - if you don't have the momentum often they don't end up in the net."
While Howard performed heroics for the visitors, Petr Cech also showed his class by twice denying former Chelsea striker Romelu Lukaku and Martinez was left to rue those missed chances.
The Spaniard said: "We were in control. We had clear-cut chances, the best ones of the game - they needed world-class saves from Petr Cech.
"It's a shame we couldn't convert the chances. It's a huge disappointment. Our performance deserved a positive result."
