Saints trailed 4-1 at the break having been caught cold by a ruthless Gunners side, with an early injury to Jos Hooiveld making matters worse.
A bright start to the second period gave cause for encouragement, but the north Londoners added another two goals to consign their visitors to a significant loss.
"It was a very poor scoreline having come away from home," First Team Manager Adkins told Saints Player
"Everyone knew that the first four fixtures were going to be challenging, but we want to win games of football.
"We've come away to Arsenal wanting to keep good possession of the football – and I thought we actually started the game brightly in that respect – but we've conceded an early goal and then lost Jos Hooiveld to a calf injury.
"That allowed Arsenal to get a head of steam up, and Alex Chamberlain gave us all sorts of problems.
"I'm a very positive person, so we'll analyse this then draw a line underneath it having learned as much as we can.
"We'll have a good week's training and get everyone together – there are no hiding places so we'll stand up and be counted.
"We've got some good additions who have come and joined us, and we are a very positive football club.
"St Mary's will be bouncing next week because it's a game we've obviously got to go and win.
"We believe that we're doing a lot of the right things, but it's about picking points up – so next week is a big three points that we've got to go and get.
"We've got to make sure that we don't build it up in such a way that everybody starts getting very nervous, but we've got to concentrate on the important aspects of the process of winning games."
Maya Yoshida and Gastón Ramírez made their Saints bows from the bench, with Yoshida replacing the injured Hooiveld inside the half-hour and Ramírez coming on at the break.
The Uruguayan almost teed up Rickie Lambert to make it 4-2 just after the interval, leaving Adkins to wonder what might have been if the frontman's shot had beaten Wojciech Szczesny.
"A scoreline of 4-1 at half time was not what we wanted, and we knew the game was probably beyond us in the respect of getting a result," admitted the gaffer.
"For the second half we looked at maintaining our KPIs and the process of passing football – playing out from the back and through the thirds [of the pitch].
"There was a notable chance for Rickie Lambert with one that went past the post, and at 4-2 who knows what could have happened?
"We had good pace, discipline and possession of the football but it's been highlighted in the games we've played already that at this level that if you turn over the ball cheaply then you are going to be punished.
"The top teams keep possession of the ball and grind you down.
"Gastón Ramírez came on having been in Uruguay and only trained with us for the first time last night, but you could see the players' eyes light up with the things he was doing in training.
"That was really pleasing because he did ever-so-well. He's got undoubted ability and a wand of left foot – he can pick out a pass and has an eye for goal.
"Playing between the lines in the number ten position, he is ideal.
"And Maya has come in having been in Japan for a couple of weeks and then he's been with us for the last couple of days so he's been introduced very early.
"It would have been great if he could have had four weeks of training, but I must say that I thought he did ever-so-well in the second half as he grew in confidence."
And Nigel reserved special praise for Saints' sold-out travelling contingent, who backed the players throughout the game despite a worsening scoreline.
"I must say that the fans were outstanding today, so thank-you very much," he said.
"It was a challenge because this was probably the heaviest defeat I've ever had, so it's not a nice scoreline and you find out about yourself.
"But all the way through the game the supporters stuck with the team because they knew it was a challenge for us.
"They did everything they could to keep lifting the spirits of the players."
Click here to watch Nigel's full post-match interview on Saints Player.