Walcott eluded the marking of Kieran Tierney to open the scoring in the first half against his former club but Pierre-Emerick Aubameyang hit back in the second.
Arsenal, though, finished on the back foot as Gabriel was sent off.
Walcott has hinted that Southampton feel they dropped two points, despite being away to a side that habitually finishes in the top six.
“I felt a lot of fear in Arsenal tonight, to be honest,” he admitted after the game.
Meanwhile, Aubameyang revealed there was anxiety in the home team as the final whistle approached.
“At the moment we're a bit nervous because we need points,” he said. “It was tough at the end but I think the team gave everything to get that point. We’re a bit disappointed because we could have won this game but sometimes this happens.”
The Gabon international striker admitted that he was pleased to break his duck of having failed to score a home goal this season.
“I'm a guy who when things go wrong I stay in my path and I work a lot. I try to do my job and give my advice inside. It's true I wasn't talking a lot these few weeks. I'm here and I want to talk on the pitch,” he said.
Mikel Arteta’s under-fire side will travel to Goodison Park on Saturday to tackle Everton in their final match before Christmas.
The Boxing Day encounter at home against Chelsea, meanwhile, is sure to be a pivotal encounter both in the direction of their season and in their manager’s long-term future.