The Gunners were held to a 1-1 draw at St Mary's on New Year's Day after scoring 15 goals in their previous four Premier League outings.
"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," Gibbs 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."
Gibbs recently joined Jack Wilshere, Aaron Ramsey, Alex Oxlade-Chamberlain and Carl Jenkinson in signing new deals at Arsenal and the 23-year-old says he would not want to be anywhere else.
"Me and the other boys committed ourselves to the club," he said. "I've always been committed to the club ever since I was given my chance by the boss.
"I've wanted to show him how dedicated I am. I hope the last few months I've done that."
Next up for Arsenal is Swansea in the FA Cup third round and Gibbs added: "We go there like it's one of our biggest games of the season.
"We need to go there and realise that this is another opportunity to get a trophy and we want to go there and win."