But had they had the strength in depth league winners Manchester City had in their squad, they could've edged Pep Guardiola's side - and they'll be keen to get closer to their rivals' level this summer.
With Granit Xhaka and Kieran Tierney amongst a number of Gunners stars linked with an exit this summer, Mikel Arteta and co need to recruit wisely to ensure they can push to win the title next season.
Injuries to key players including William Saliba and Gabriel Jesus throughout the campaign seriously hindered the north Londoners' chance of securing their first league title since 2004.
But should they keep hold of their key stars whilst also bringing in some new talented additions, the Gunners could be on to a winner.
So which linked players should Edu sign this summer to add to their starting XI and finally get Arsenal that Premier League title? talkSPORT.com takes a look...
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Declan Rice
Everyone's talking about West Ham's skipper after he lifted the Europa Conference League trophy with the Hammers on Wednesday night.
The England international has been heavily linked with a move away this summer for some time, and Hammers owner David O'Sullivan has now exclusively told talkSPORT Rice will leave the club this summer.
O'Sullivan expects offers to come in for the talented midfielder straight away and talkSPORT understands Arsenal are favourites to sign him.
Jorginho has only one year left on his current deal and Thomas Partey's injuries at key points of the season mean 24-year-old Rice will be a perfect addition, even if he does come with a hefty price tag.
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James Maddison
Despite wingers Bukayo Saka and Gabriel Martinelli being joint top scorers for Arsenal this season alongside Martin Odegaard, it's no secret Arteta wants some more speedy wide players.
After missing out on Mykhailo Mudryk, now the Gunners have been linked with Leicester playmaker James Maddison, and he could come in on the wing, just like he does for England.
The Foxes talisman still has a year on his current deal, but following the club's relegation to the Championship it seems inevitable Maddison will be on his way with him aiming to represent his country at Euro 2024.
Maddison won't come cheap, and he's also linked with rivals Tottenham as well as Newcastle. But Arsenal should be willing to pay to ensure an injury to their current wingers or midfielders won't be detrimental to their campaign, never mind the increase in attacking threat.
Joao Cancelo
Much like Maddison, the Man City's full-back could help add experience into Arteta's youthful side.
The 29-year-old's loan stint with Bundesliga champions Bayern Munich has come to an end and a return to the Etihad Stadium looks unlikely after falling out of favour with Guardiola ahead of the move.
Arteta is reportedly interested in signing him this summer, which would see him reunite with former City teammates Oleksandr Zinchenko and Jesus.
The Ukrainian has already proved to be a great option for Arsenal at left-back. But with Tierney heading for the exit door, the Gunners' full-back options would certainly be boosted with the addition of the Bundesliga winner.