Arsenal travel to the League Two side at Highbury Stadium on Tuesday, looking to build on their 2-0 victory over Ipswich Town in the previous round.
The Gunners have never faced Fleetwood in a competitive fixture and will be wary of an upset against lower-league opposition.
Arteta knows the danger of underestimating opponents, having experienced Arsenal's penalty shootout defeat by Bradford City in the League Cup in 2012, when he was an unused substitute.
"Our reputation, our pride, everything is in play," the Arsenal manager said.
"Every time you play a football match, and especially against a team in a different division, respect the game, respect every opponent because they deserve to do that, and then try to win and try to play a bit better than them.
"We all have one (upset) at some stage. We know the risk, and in football, things can get very equal the moment you are able to match certain things.
"That's why our basics and habits have to be through the roof to be able to win the game."
Viktor Gyokeres is another player looking to make an impact after starting Arsenal's 2-0 Premier League victory over Everton, having also featured against Ipswich in the previous cup round.
The Swedish striker is still waiting for his first goal of the season, but Arteta remains encouraged by his overall contribution and believes persistence will bring rewards.
"He's done a lot of good things," Arteta said after the Everton match.
"We need to keep insisting. I think he had a really good contribution in Munich as well when he came on, he helped us to change the game, and that's what we need from all of them."
Max Dowman could also feature against Fleetwood after earning Player of the Round recognition for his two-goal contribution against Ipswich.
The teenager has impressed Arteta, who believes Arsenal will need contributions from across the squad as the season progresses.
Cristhian Mosquera is another option after recovering from the injury he suffered during Arsenal's victory at Aston Villa in August. The defender has since returned to the matchday squad for the club's last three games.
Arteta praised Mosquera's performances and highlighted the importance of having different options available.
"When he has played, he's done really well. We have won some big games playing with him, and we need him," he said.
The Arsenal manager also pointed to Myles Lewis-Skelly and Dowman as players who could make important contributions.
Speaking about Dowman's recent involvement, Arteta added: "Today he came in [against Everton] and he seems to be very comfortable. In this kind of position. We're going to need everybody. I'm convinced of that."
Xabi Alonso has backed goalkeeper Mike Penders to recover from his costly mistake against Tottenham Hotspur, confirming the young Belgian will start Chelsea's Carabao Cup clash with Liverpool at Anfield on Wednesday.
Virgil van Dijk has challenged Liverpool's attacking players to deliver more following Mohamed Salah's departure, although the Reds have shown encouraging signs of adapting to life without the Egyptian forward.
Unai Emery admits he would relish the chance to recruit some of football's finest talents but insists he is enjoying the task of building Aston Villa into a team capable of challenging at the highest level.
Mathys Tel delivered a moment of brilliance to seal Tottenham Hotspur's 2-0 victory over Chelsea at Stamford Bridge on Saturday, with the young forward's superb solo goal highlighting his growing influence under Roberto De Zerbi.
