The Gunners came into the Group B clash fresh from a disappointing 2-1 loss to their London rivals at Emirates Stadium on Saturday.
Arsenal manager Arsene Wenger spoke about making amends for that defeat in the build-up, but this evening saw his side stutter against the Greek champions.
The Frenchman was in the stands as he is in the midst of a three-game touchline ban and his man on the ground, Bould, knows the 3-1 scoreline flattered the hosts.
"We've won the game, it is a great result for us," the assistant coach said. "We made it tough.
"They were actually, I thought, very good. Their organisation was excellent and they made it tough for us.
"I think we improved in the second half with the ball, but we looked a little bit nervy, I have to say, at times and overall we are delighted.
"I think it probably affected our confidence a little bit getting beat when we felt perhaps - even though we didn't play so great - we should have got something from the game.
"Maybe there was a little bit of a carry-over, but we're hoping now that we've won that has gone, done and dusted, and we get back on track."
Despite a shaky opening 45 minutes, Gervinho fired the Gunners ahead three minutes from the break with a lovely strike from the edge of the box.
Kostas Mitroglou levelled in first-half stoppage time, but Arsenal went on to collect the three points thanks to goals from Lukas Podolski and substitute Aaron Ramsey.
Gervinho set up Podolski's goal as well as netting his own and was given the man-of-the-match award for his performance.
The Ivory Coast international has been deployed as an out-an-out striker in recent games and has impressed in the position, leading some to ask if the transition from wide man can be as successful as the one made by club legend Thierry Henry.
"Well, if he gets anywhere Thierry Henry we'll take that all day long," Bould said. "Number one, he is scoring goals so his confidence is sky high.
"Number two, I think his link play is gradually improving. I think he set Santi [Cazorla] up quite a few times over the last few games.
"He is learning his trade there. I don't think he has played there an awful lot and he is a danger with his pace and movement at times. He could be a top player."
One notable absentee from tonight's matchday squad was German centre-back Per Mertesacker, who Bould revealed is the latest Arsenal player to be struck down by illness.
"He was ill this morning," the former defender said. "He has a bit of a virus I believe so that's where he is at. We're hoping he is fit for the weekend.
"I am told it is a different virus each time so I don't know if its in-house, I've got no idea.
"We've had about four of them ill over the period of about two weeks."
Bould also had to field questions about his side's defence, which, after collecting clean sheets in Arsenal's first three games, was breached for the sixth successive game in all competitions.
"It was always going to be that way," Bould said. "There was only one way to go.
"We got three clean sheets and we've done OK. We haven't had an awful lot of goals against.
"The goals that have been against in the main have been set pieces, which we're all disappointed and think we can improve. Things are looking OK."
Things are looking less rosy for Olympiacos as they sit bottom of Group B with no points from their opening two matches.
"The truth is the result doesn't represent how Olympiacos played," manager Leonardo Jardim said.
"I thought we played well and we had three clear opportunities to score a goal.
"That gives us a lesson that in this competition the fact that you have to take your chances is absolutely vital.
"The second part of the game Arsenal improved. We remained well organised and we had a good attitude.
"We tried to stay at a high level which we did with the exception of the last 10 minutes."
Arsenal center back Thomas Vermaelen admitted that the win was a hard-earned one and revealed that Bould
"Yeah I think in the first half [it was a struggle]," Vermaelen told Sky Sports. "The second half was better, but in the first half we were a little bit sloppy in the passing, we lost a lot of balls. We started well, but the first half was not great.
The Belgian also hailed the importance of winning their first two games in the Champions League and praised the in-from Gervinho.
He continued: "It gives us a lot of confidence, getting six out of six [points]. That's really important. I think the most important thing is to win your home games in the Champions League, and we won an away game at Montpellier so we want to keep it going.
"[Gervinho] is doing great. He had a great pre-season as well. And now you can see in the matches, he's scoring a lot of goals, he's quick, he's quite busy, so I'm happy for him."