The Saints are in danger of slipping out of the European spots after a run of just one win in six matches, which has left them clinging on to seventh place in the Barclays Premier League table.
Only finishing fifth or sixth will guarantee the south-coast club a place in Europe's secondary tournament, while seventh will also be enough if Arsenal win the FA Cup
Southampton host Aston Villa on Saturday, knowing victory will move them four points clear of Swansea in eighth, before Garry Monk's side entertain in-form Manchester City on Sunday.
"If we win, we will have a good possibility to achieve the sixth or the seventh position in the table and that makes the season a special one in my opinion," Koeman said.
"It's always difficult because if someone offered me a paper in pre-season to finish eighth or seventh in the table, I would have asked, 'where can I sign that paper?'
"But, of course, the feeling in the last part of the season is also important and, of course, you have to look back to the whole season.
"It will be a good season for Southampton but if we don't reach the sixth or seventh position, you end the season with a little bit of a different feeling."
The merits of qualifying for the Europa League are questionable given the number of extra matches the competition demands and the difficult of balancing Thursday night games with league fixtures at the weekend.
It has been suggested teams like Tottenham and Liverpool would stand a better chance of finishing in the top four if they avoided the tournament next season, but Koeman insists European football would be something to savour at St Mary's.
"Maybe for a big club the Europa League is not what they want - they want Champions League football," Koeman said.
"But for us - and I think for Swansea, I think for Stoke - it's a big achievement to play in Europe.
"There is no issue that we will do everything to reach that possibility.
"What will happen afterwards, we will see how we have to handle that, but it will be a great achievement for the club if we reach European football."
Southampton may need a deeper squad to handle the additional workload, but Koeman insists he will continue to prioritise the club's youth system when looking for new players.
"Would we have to change our transfer plans? Maybe," the Dutchman said
"But first we will always look to the under-21 players because that's the future of the club
"We also have some players on loan - we have to make decisions about those players.
"It's possible that we need one or two players more and more numbers in the squad if you play European football.
"But first we have to win and then we will see what happens in the summer."
Source : PA