After Geoff Cameron had cancelled out Aaron Ramsay's fifth-minute opener, Stoke were undone courtesy of goals in either half from Per Mertesacker and Bacary Sagna.
But despite the defeat, Hughes, who took over from Tony Pulis in May, was encouraged with what he saw from his side.
"We've taken huge strides in a short space of time," said the Stoke boss.
"The more games we can play when we're still very much a work in progress will help us.
"We need to keep the performance level going in the right direction and, after a difficult opening period where we've played Liverpool, Manchester City and Arsenal, we've come through that period in good heart and full of confidence."
Hughes felt his side were capable of getting a result at the Emirates Stadium while the scoreline was at 2-1 in the hosts' favour.
However, the timing of Arsenal's third goal was crucial according to the Stoke boss, who was encouraged by the style his side adopted in the second half.
"I thought we showed good courage and determination to get back on level terms and at 1-1 we're still very much in the game," he continued.
"We showed a lot of control and possession in the opposition half, which is what we want to do this season.
"At 2-1, I felt the team most likely to score was probably us but the third goal took the wind out of our sails and came at a poor time for us."
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