Arsene Wenger was serving the first of his three-game touchline UEFA ban - and would have been fuming from the stands when captain Thomas Vermaelen gave away an early penalty, although replays suggested the foul was probably just outside the box.
However, the Premier League club, unbeaten in the domestic campaign, responded magnificently and were soon level through a fine finish by German Lukas Podolski.
Before the French side, making their Champions League debut following last season's brilliant Ligue 1 campaign, could recover, Arsenal swept ahead in the 18th minute through Gervinho.
Although the hosts rallied after the break, with lively winger Remi Cabella hitting the crossbar and goalscorer Younes Belhanda missing a great chance late on when he fired straight at stand-in goalkeeper Vito Mannone, the Gunners closed out a battling victory.
Bould said afterwards: "I am not sure I enjoyed it. I have got a headache and a half.
"It is tough, a different pressure than I have been used to taking the Under-18s - but we won and we had a great result."
Bould felt it was another encouraging display from the squad.
"It was difficult. I thought we were excellent in the first half - we kept the ball and kept the crowd quiet," he said.
"We looked a little bit tired in the second half, because it was very humid and the crowd got behind them.
"It is quite an intimidating place to come and play so we are glad to get the result.
"We have had a decent start to the season and we have kept the run going so it's important all round, for the whole season.
"We have got great team spirit and I think that was evident tonight. Everybody is digging in and things are looking okay."
Podolski netted his third goal in as many games tonight, with a neat finish after quick passing on the edge of the penalty area.
Bould said: "Podolski has made a real impact. I have to say I've not seen many finishers as good as him - ever, right foot, left foot, they always go in at 100 miles per hour in training.
"He is a good trainer, a good boy and has really added something this year."
It was, though, another barren evening for Olivier Giroud, the £12million summer signing from Montpellier.
However, Bould insisted there was no cause for concern.
"Olivier did a really good team job for us tonight. He works really, really hard for the team - at set-pieces he is fabulous," said the Arsenal assistant manager.
"He had one chance at the near post that was difficult. Olivier is a really hard-working boy and I am sure the goals will come."
Much has been made of Bould's arrival to the first-team coaching staff, with the Gunners having only conceded one Premier League goal, and that in the 6-1 trashing of Southampton last weekend.
However, the former Arsenal defender insisted it was not all just about him.
"Any coach will tell you it is about having good players and we've got some good players who want to work, so far, so good," he said.
"Everybody's spoken about myself, but Neil Banfield gets missed and he does a good job, too.
"Everybody's working hard, the players and the coaches, and I think that's why we are doing okay at the minute."
Arsenal now head to Premier League champions Manchester City on Sunday.
Bould said: "We will go there with a bit of confidence.
"It is better being this way, but it is a proper test.
"It is where we want to be and hopefully we can come away saying we did okay again."
Montpellier coach Rene Girard felt his team could take some positives out of their Champions League debut.
"I have some regrets but also some satisfaction," he said.
"Maybe we were a bit too shy in the first half, then looked more determined.
"We had a few chances to equalise, but at this level when you make some mistakes, you will pay for it.
"We can be proud, because apart from these two minutes we managed to play well against this top European team like Arsenal, so there can also be some positives from this performance."
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