"I'm delighted," Hughes told Sky Sports. "I thought we were excellent from start to finish.
"We needed to make sure Arsenal did not get a tempo to their play and rhythm to their passing and we didn't let them do that.
"We were always a threat today and created a number of chances and on another day we would have converted each and every one of them.
"To win 3-0 against one of the 'Big Four' you have to play really well and today we've done that. I think we deserved it."
Hughes reserved special praise for Ireland.
"Stephen's finished it superbly well and he's having an outstanding season," Hughes added.