After his appointment in 1996, Arsene Wenger guided the Gunners to three Premier League titles and four FA Cups within his first nine years with the club. However, that was succeeded by a nine-year period without a trophy prior to the 3-2 victory over Hull City at Wembley 10 days ago.
Now, though, Seaman believes that the recent success can act as a springboard to further achievements over the coming campaigns.
"They've been feeling the pressure [to win something] for a long time, but now they've got medals around their necks. It's a great feeling and they will always have that for the rest of their lives," he said. "My first season at Arsenal, we won the league. I was lucky because that pressure of not winning anything didn't build up. All the trophies that I won came after only short spells without success, so there was never much of a burden on the team.
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"They moved to an awesome new stadium not so long ago, but didn't have a trophy to go with it. Now, the shackles are off and they can take that confidence to go on to win some more medals because it's the best feeling in football."
In spite of winning the FA Cup, there remain some Arsenal supporters that feel Wenger should still step aside, insisting that returning the club to winning ways would have been the perfect way for the 64-year-old to bow out, while making way for a manager with a fresh approach.
However, there are reports that the Frenchman is to sign a new contract to extend his 18-year stint at the Emirates Stadium - rumours that have pleased Seaman, who has warned fans "to be careful what they wish for".
"I've defended Arsene all along, even when there was a number of fans calling for him to be sacked. The fact that we've qualified for the Champions League and won the FA Cup means that it has been the most successful season in nine years," he added.
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"Look at Manchester United. Sir Alex Ferguson may not have been sacked, but sometimes it doesn't work when a new man comes in. Those that still want Arsene out need to be careful what they wish for. With Arsene there, he's got control and he knows what to do. Sometimes he can be stubborn, but I like that. He knows what he wants and by winning this trophy it has lifted a lot of the pressure off of him and the team."
With Wenger almost certain to remain at the helm, attention has already turned to which players will be targeted to bolster the squad.
Assessing the areas of the pitch that are in need of improvement, there is one position in particular that Seaman has highlighted as requiring strengthening if Arsenal are to challenge for trophies again next term.
"There is still work to be done and Arsene will know that. He's going to need to bring in a couple of bigger and better players. They've got Champions League football to offer and now that they've added a trophy as well, it will be even easier to attract players [to the club]," said the 50-year-old.
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"When Mesut Ozil come in, he was a great signing, but not only did he bring in his quality, he raised the squad's quality. They wanted to prove to him that they could play as well - that's what happens. Players want to show new signings that they are just as good as them, if not better. It raises the standard throughout the team."
One player that does not need replacing is goalkeeper Wojciech Szczesny, according to Seaman, who spent 13 years between the posts for the North Londoners. "He had his best season for Arsenal. If he keeps improving like he is, the shirt is his and he should stay there," he said.
David Seaman and top female freestyler Laura Biondo are working with Mini Babybel this summer, offering people the chance to win one of 15,000 free mini-footballs through their exciting on-pack promotion. Former England international David is encouraging families to get out and play football and be inspired by the skills demonstrated by Laura in the latest Babybel video. For more information visit www.babybel.co.uk.