The Gunners needed an own goal from Southampton's Guly Do Prado to equalise Gaston Ramirez's opener as they ended their festive fixture list with a point.
Arsenal scored 15 goals in winning their four Barclays Premier League games leading into the clash with the Saints and Gibbs was frustrated not to make that five.
"It was disappointing to break our winning streak because four on the spin left us feeling good and we were so hungry to get three points," he said.
"It was disappointing to only get the draw but we have to move on to the next game.
"(Near the top of the table) is where we expect to be, even more. But the winning run gave us a good lift at this stage of the season because the games come thick and fast at this time of year."
Arsenal boss Arsene Wenger did not feel his side were at the races at St Mary's and Gibbs knows playing well regularly is important.
"Consistency over the whole season, we're looking for that," he said.
"Over this period I've been impressed with everyone and the effort they've put in, credit to the boys.
"But we are looking for more consistency over the whole period of the season."