Arsenal stopper Wojciech Szczesny is unhappy after the Gunners failed to mount a sustained challenge for the title in the final stages of the season.
The Gunners led the table for major parts in the first half but their challenge petered away owing to a barrage of injuries to key players and their failure to withstand the pressure from teams in the top half of the table.
Heavy losses against Liverpool, Chelsea and Everton in the second half stalled their title challenge while a defeat to Stoke City and a draw with Swansea City took away any chance they had of putting in a proper end to their campaign.
However, the Gunners have secured the fourth spot and have an FA Cup final to look forward to in May where they face Hull City at Wembley in a bid to end their nine-season trophyless run.
Everton were threatening to take Arsenal to the edge but failed to keep up the challenge as they dropped points against Crystal Palace, Southampton and Manchester City in the run-in after beating the Gunners.
However, Szczesny is not satisfied with the fourth place and wants the Gunners to come back stronger next season and seize the initiative.
"I think it's good to sign off with a win and sign off in front of our fans but with two games to go we had nothing to play for at home and I think we shouldn't really be in that position. We should be fighting for the title," Szczesny told www.arsenal.com.
"Of course [there's a sense of what might have been]. I believe that we should be in a position to challenge to win the Premier League and maybe Sunday would have been a completely different atmosphere if we had kept going the way we were at some point.
"I never considered fourth place before the start of the season as a successful season and a good position. I play for Arsenal Football Club because I want to win the title every year.
"Obviously at some point, when you lose games and you lose the chance to fight for the title, then the new challenge is to secure the Champions League spot and that was the aim this season, but I wouldn't have taken it before the season.
"We dropped some important points and lost games and had to finish fourth when we weren't probably the favourites to finish fourth. At least we managed to do that for our fans and hopefully we'll manage to get the FA Cup for them," he added.