It led boss Arsene Wenger to express anger after the match, but Szczesny remains positive.
"I think Southampton defended much better than Newcastle did the other day," the Poland international said. "You have to give credit to them a little but we are still disappointed with the result.
"We were confident of getting the three points and, unfortunately for us, we have not been able to.
"We are on a good little run. We won four league games on the trot but didn't get the three points here, which is the most important thing.
"We hope to do well in the FA Cup and then carry on our run in the Premier League."