Adkins' side have lost all four of their matches since returning to the top flight and were given a hiding today as they failed to cope with the Gunners' speed and directness.
"We just played a very good team and the big thing is - we highlight it all the time - if you have good possession of the football and you turn it over cheaply, the players at this standard are going to punish you," the Saints manager said.
"Obviously Gervinho and Alex Oxlade-Chamberlain are two talented football players. They were ruthless today.
"When the fixtures came out, people were looking at Man City, Man United, Arsenal - three games that on paper we would probably get a good chasing in.
"Today we have come out on the back of a poor scorelines, but from my point of view it just highlights the standards in the Barclays Premier League and what we have to aspire to.
"When we look at it, I think we actually started the first five minutes all right. We kept good possession of the ball and that is what we looked to do.
"But when you score an early goal anywhere, it gives the opposition the upper hand.
"We'll analyse the goals ourselves tomorrow and there are probably things you think you could do better on."