The Gunners have opened a new chapter after 22 years under the guidance of Arsene Wenger.
The end of his iconic reign saw the club slip out of the Champions League, with Unai Emery charged with the task of returning the club to the European elite while challenging for major honours.
He has added veteran full-back Stephan Lichtsteiner to a squad inherited at Emirates Stadium, but Seaman feels more additions are required over the summer in order for Arsenal to be competitive.
The ex-England international told Omnisport: "You’ve got to progress on the season before and we were out of the top four and we were getting left behind by quite a few of the big clubs.
"We need to regroup, have a little restructure of the team and then push on, get into the Champions League again and try and improve on that each season.
"It’s not going to be easy because the big guns are quite a way ahead at the moment. We need steel in the team.
"We need a couple of defenders, dominant defenders, and a dominant midfield player.
"I think the forward side of it, you can leave that alone because we’ve got a lot of firepower there. I’m just a little bit worried about the defence and the art of defending."
Emery appears to be trying to address those issues, with a deal for Borussia Dortmund defender Sokratis Papastathopoulos reported to be close.
The Gunners are also being linked with several midfield targets, while there remains a desire to tie Wales international Aaron Ramsey down to fresh terms.
Attention is, however, about to shift to World Cup matters, with it unlikely that deals will be done for those competing in the global showpiece until their respective campaigns come to a close.