The defender said the result could give the League Two side a lift, but insisted they must show the same commitment when the attention shifts back to their domestic campaign.
“The champions of England coming to our patch, we always knew it was going to be a tough game, we always knew we were going to have to grind out a result.
“I think 1-1 was probably a fair result over 90 minutes, I think we did what we needed to do, I think everyone stuck to the game plan, but yeah, it gives us so much confidence, so much motivation, and it brings us lads closer together because we know we can trust each other arguably against the best players in the world at the moment.”
Fleetwood took the lead through Aaron Loupalo-Bi in the 21st minute before Viktor Gyökeres equalised five minutes into the second half. Arsenal controlled much of the possession, but the home side held on through the remainder of normal time and then converted all five penalties to win the shootout 5-3.
Batty said the occasion had been a special one for the squad, but challenged his team-mates to make sure the performance was not a one-off.
“We have to replicate that every game. Our league form hasn't been as good as what we wanted it to be, and for some reason, cup competitions give everyone a bit more fire in the belly. We just came up with some magical moments, and this one, is one to tell the grandkids.”
The defender acknowledged that Fleetwood had expected Arsenal to dominate the ball. Their plan was to stay organised, communicate and support each other when the pressure increased.
“We knew they were going to come here and dominate the ball. We're not silly, we know what we are, we know what they are. Obviously, when they got the goal early in the second half, you're thinking 'oh god, here we go', but I think the resistance, the communication, and the culture of the lads.
“Everyone is just doing a job for each other, fighting for their own place, which is what they need, and we need to go onto Saturday, and carry that momentum and confidence into the game to get three points. We knew we would give [Arsenal] a good game on our patch, and we knew the crowd was going to be there for us.”
Speaking to BBC Radio 5 Live, Batty also urged supporters to bring the same energy to Saturday’s League Two fixture against Bristol Rovers, despite the difference in profile between the opponents.
“We have struggled. We're not known as a big club in League Two, and we get a few thousand fans each game.
“The buzz around town, the fans didn't shut up all game, and that's what we encourage [everyone] to bring on Saturday.
“Just because it's Bristol Rovers on Saturday and not Arsenal at home, why can't we replicate that and get 5,000 fans behind us every game and give us that momentum. Every single one of us is so happy and proud of all the fans that turned out today.
“That's exactly what we need. Because without them, we would have struggled in the moments when they were giving us an extra lift. You think bloody hell, there are a lot of people here supporting me, wanting me to do well. It's unbelievable for the town. I don't think we should be scared of anyone, or any team now.”
For Batty, Fleetwood’s upset will mean most if the team can turn a landmark cup night into a springboard for their league form. The challenge now is to carry that belief into a very different fixture on Saturday.