Southampton have been in contention for Champions League qualification this season, and Fonte says they are disappointed not to have hit that target.
The Saints have performed beyond the expectations placed upon them at the start of the season. After losing several players last summer, under Ronald Koeman's management they have been in contention for a European spot for much of the season, and could qualify for the Europa League this weekend if they leave the Etihad Stadium with a famous victory.
But after spending much of the season in the Champions League places, which saw Southampton as high as third in January after beating Manchester United at Old Trafford, Portuguese international Fonte is quoted in the Daily Echo as saying: "I don’t think we overachieved at all.
"We did a great season, yes, considering everything we went through before, but I really believe we could have gone a little bit higher.
"I think we honestly could have even finished higher. We lost three or four games that we shouldn’t really have lost.
"I know this is the Premier League and it’s the hardest league in the world and anything can happen, but I really believe that at least four wins we could have got instead of four defeats that we had, and that would have put us you know where - in the Champions League."
It is testament to the job Koeman has done at St Mary's this season that they are disappointed not to be looking forward to Champions League football next season, and also indicates just how rapidly standards and expectations within the club have risen – which should give the Saints fans plenty of cause for excitement.
If Fonte's comments reflect the mentality of the rest of the squad, that they believe there is room for improvement and they feel they should have more points this season, then that is a solid foundation upon which to build going forward.