The Saints went into the match having failed to win any of their last six games, but they swept the Premier League title favourites aside at St Mary's on Boxing Day.
"It was a fantastic performance against a good Arsenal team - that's a big compliment to the players. We caused them lots of problems up front through Mane and Long. Perfect performance today," he told BT Sport.
"Normally I keep criticism of my players inside but sometimes people need to know what the manager is thinking. We showed fantastic belief in everybody and showed how good we are today if we play at our level.
"The second half was far better than the first, some good goals and maybe more chances to score more."
Southampton remain in 12th place despite the victory, while Arsenal are still second having missed the chance to move top of the pile.