The exchange followed the 61st-minute opener, when Jannik Schuster met a Mikkel Damsgaard corner at the back post and headed it across to Jaidon Anthony, who was left unmarked to nod in.
Martínez barely moved during the set piece, and Henderson appeared annoyed that his goalkeeper had not come for the ball. Anthony had found space with three Chelsea defenders nearby, while Henderson himself had been marking nobody.
The Daily Mail adds that the pair were seen comforting each other at full time, and that Henderson also remonstrated with defender Maxence Lacroix at another point.
Chelsea never recovered. Igor Thiago doubled Brentford's lead on 83 minutes, tapping in the rebound after Martínez had saved from Kevin Schade, and substitute Fábio Carvalho added a third in stoppage time. It left Xabi Alonso's side having conceded 12 goals in five Premier League matches.
Martínez, 33, joined from Aston Villa late in the window for £7.5 million, brought in to solve a goalkeeping problem after Robert Sánchez's errors on the opening weekend. Sánchez is now on loan at Como. Henderson, signed from Brentford for his experience and leadership, was making his first start for Chelsea against his former club, having arrived while recovering from a broken arm suffered on England duty.
Former Chelsea captain Gary Cahill, speaking to Sky Sports, saw a wider problem.
"There is a certain element of fragility.
"Once they've conceded that set piece, you don't want it to be a mindset but it is a 'here we go again' type scenario.
"I'm sure the manager will address it in videos and on the training ground. Obviously, as a goalkeeper and a back four, you feel a big responsibility when goals are going in.
"The only way you can get out of that is by working hard together and making sure you're harder to play against, and be more ruthless.
"There just seems to be a kind of softness at the minute in terms of the way they concede goals. You have a few weeks now during the international break, although some of them won't be there, but they will have time."
Alonso himself called for patience, according to Sports Illustrated.
"It's a process," he said. "It takes time for them to feel it and at the moment we are not feeling it fully to compete for the whole game."
The Spaniard is trying to implement a back three with wing-backs, a system that has often proved a risk in the Premier League. It has worked for Chelsea before: Antonio Conte switched to it after a 3-0 defeat at Arsenal in September 2016, and his side went on to win 13 league games in a row and take the title by seven points.