Marcelo Bielsa's squad exited this year's Carabao Cup competition at the fourth round stage on Tuesday night, losing 2-0 at the Emirates.
Leeds were back in midweek action following Saturday's draw with Wolves as the Elland Road outfit opted for a strong line-up in the capital.
United created numerous first half chances against their hosts, though failed to make Arteta's men pay as they deployed several quick counters and forced Bernd Leno into a number of saves.
Bielsa's outfit were unable to recreate their strong showing in the second half, conceding twice as substitute Calum Chambers and former loanee Eddie Nketiah both found the back of the net to send Leeds out of the tournament.
Arteta - who also opted to put out a first team heavy starting line-up on home soil - admitted Leeds caused their hosts problems before his team took over after the interval.
"A really good performance over a team where the manager in every action is so committed," Arteta reflected post-match.
“We understood the game and what we had to do, we did this the right way. They gave us some issues, they always do, but we created a lot of shots and situations without being very clinical, we adjusted a few things at half time and we were better and stronger.”
Asked about former Whites loanee Nketiah, Arteta said: "I have no doubt over what he can offer. Whatever you throw at him, he wants more. I'm delighted to see the performance he had, because he totally deserved it."
The Gunners also saw Ben White - a familiar face to Leeds fans - leave the field of play early and his manager revealed the reason why afterwards.
"There's a bug going around," Arteta added. "Ben had it for the last day or two. He wasn't feeling great so we decided to take him off."