Cardiff did manage a consolation when Sol Bamba bundled home, but the four-goal margin was restored when Deeney scored his second from Will Hughes' cross in injury time.
Gracia said: "It was a very good performance. To win here is not easy. To win like we did today was outstanding. I am very proud of all my players.
"Playing away we are getting good results. We knew it would be a hard game. They changed their shape and they tried to do more compact and defend better but we found the spaces and scored different goals - in counter-attack and in possession games,
"Our players showed good qualities and scored lots of goals so I am happy. Before the game we knew it would be important to have mobility and attack the spaces.
On Gerard Deulofeu's hat-trick, he said: "It was important the three goals but in my opinion it was more important to assist after the three goals to be generous and pass it."
On Cardiff's penalty shout, Gracia added: "I understand. They can be angry with that but I prefer to not say anything about that. We played very well, scored five goals and dominated the game. We deserved this victory. Now we focus on the next game and we try to do our best."