The Gunners fell behind early at Southampton as Charlie Austin gave the hosts a third-minute league following some indecisive Arsenal defending.
Eight days earlier Arsene Wenger's side found themselves 2-0 down to Manchester United with just 11 minutes on the clock.
United went on to win that game 3-1 while Olivier Giroud came off the bench to head home a late equaliser to earn Arsenal a share of the spoils with a 1-1 draw at St Mary's.
Those dropped points leave Arsenal 17 point adrift of leaders Manchester City and a point outside the top four and Cech knows the sluggish starts need to be eradicated.
"One thing that is really gutting is that we lost the game against Man United in the first 10 minutes," the goalkeeper told the club's official website.
"We could have been 3-0 down after 10 minutes again (at Southampton) and I think this is something we need to improve.
"In this league, if you give other teams the advantage in the first five minutes, you make it far more difficult for yourselves.
"We were lucky to get a point, even if we deserved to get one in the end, because we put them under pressure
But we wanted all three"
Southampton, who also hit the bar through Oriel Romeu, appeared to be on for one of their better results of the campaign to date.
Austin hit his fourth goal in three starts to put Mauricio Pellegrino's side on course for a place in the top-half of the table, only for Giroud to strike late on.
"I was delighted with the goal, but it was just instinct really
It got us a great start, but it's one of them where we should've got the three points," Austin told southamptonfc.com
"We've got one and in hindsight, if we'd drawn against Man City we'd be four games unbeaten.
"It is a sense of massive frustration
We started off like a house on fire, with four chances in the first seven minutes, but we needed to get the second goal."
Saints entertain Leicester on Wednesday night as former boss Claude Puel returns to the south coast following his year in charge of Southampton last season.
"We'll go again - we've got big games coming up and a quick turnaround with Leicester at home, so hopefully we can give a good performance again," Austin added.
"I feel like I'm going to get chance after chance, so I'm putting myself in the right positions and luckily I've been putting the ball in the net."
Source : PA
Source: PA