The Gunners found themselves 2-0 down after just 16 minutes at Stamford Bridge after the visitors failed to gain a foothold in the game.
Walcott, who halved the deficit in the 58th minute with a cool finish, believes Arsène Wenger’s men need to show the same character they displayed in the second half right from the off if they are to climb up the table.
“We didn’t really start until the second half,” Walcott told Arsenal’s website.
“It’s a shame that we conceded two sloppy goals and then woke up a bit. We need to show that character and desire to win from the start, not when we concede a goal.
“That is the disappointing thing. We dominated the second half and it is just a shame that we could not get the equaliser that we probably deserved.
“There were some positives to take out of it, but we need to start learning from the mistakes that we have made.”