Bristol, also coached by former All Black and Samoan international and Blues coach Pat Lam, finished the first block of England's Premiership on top of the ladder.
Having already marked Remembrance Day with a pre-game ceremony, Luatua said after his side fought back for the win, "You mention the word courage, but for us, we're just doing our jobs. Courage was all the guys who fought in World War One and World War Two, that's why we are here today, so thank you to all of the armed services, past and present."
Luatua said his side's effort in winning achieved the goal they had set for themselves.
Down 0-17, the made the most of a yellow card for Exeter's halfback Nic White with 17 minutes of the game remaining.
"It was a tough ask, but at halftime the message was pretty calm from everyone.
"We all knew that, if we just did our jobs, we could come away with the result. It took us the whole 40 minutes of the second half, and we came away with the result," he said.
Now he wants the side to build on their season to date by carrying their form into the European Challenge Cup campaign against Zebre at the weekend.
"It was one of our goals coming into today.
"We came here to try and get a win, we did that, and it's pleasing to see, at the end of it all, that we're at the top of the table. So, we'll regroup, looking to Europe next week," he said.
Lam said after the win which was the third biggest comeback in Premiership history, "It wasn't our best rugby, but it was top-shelf in terms of commitment.
"Our errors and poor discipline allowed Exeter a lead, but at halftime we had to take two breaths and start again.
"The only way back from 17-0 down is to play with team work.
"We are proud of the fact that we are on top. It's huge for our growth. It's a big win and I was delighted that Exeter were fully loaded with their England internationals. Not many teams will put 20 points on them without scoring," Lam said.