The Gunners goalkeeper scored an unfortunate own goal to put Saints ahead in their Premier League clash at the Emirates Stadium before Arsenal captain and birthday boy Laurent Koscielny levelled with an acrobatic overhead kick.
The game looked set to end all square until referee Rob Madley awarded an injury-time penalty to the hosts, having allowed play to continue despite Koscielny lying prone in front of the Southampton goal with a head injury.
Santi Cazorla scored from the spot to seal a 2-1 win and give Arsene Wenger's men back-to-back league victories either side of the international break.
Next up for Arsenal is their first Champions League game of the season, a tough trip to French champions Paris St Germain on Tuesday night.
And Cech admits there is room for improvement in Arsenal's game as they look to avoid the kind of start they endured in last season's group stage when they lost their opening two games to Dinamo Zagreb and Olympiacos.
"I think we are not 100 per cent yet," he told Arsenal TV.
"Our game is not as fluent as it could be and it should be
But I think we are getting the results that we need and this is the most important sometimes when you are playing and you know not everything is happening the way you want, that you find a way to win games.
"Obviously we did so, so we are happy with the three points and we go game by game and try to improve every day.
"I think our reaction (to going behind) was very good, we got a goal back in the first half, we tried to push for the winning goal
It came in the last minute but I think we were aggressive and we were searching for it so in the end we probably deserved a little bit of luck back."
For Southampton, they remain without a win under new boss Claude Puel and sit in the bottom three having taken two points from their opening four games.
Summer recruit Nathan Redmond again operated in a forward role and admits it was painful to lose in such circumstances.
"It's devastating because of all the hard work we put into the game," he said.
"To not come away with anything due to a controversial decision is devastating
We had good spells with a good 30 minutes and we faded a little where we took our foot off the gas, but we were always in the game and looked like we were going to score.
"I think if Shane Long had put his chance in one on one then it's a different game, but those situations and little moments in the game are what define them
We've just got to pick ourselves up and go again next week."
Source : PA
Source: PA