The Saints cruised to a 4-2 Premier League win at relegated Villa to keep the pressure on Liverpool, who blew a 2-0 lead to draw 2-2 with Newcastle.
Dusan Tadic's double and goals from the impressive Shane Long and Sadio Mane kept their slim Europa League chances open.
They are eighth in the Premier League table, a point behind Liverpool and two adrift of West Ham, and Koeman wants to keep the pressure on their rivals
He said: "What you like, at the end of the season, is to play for something, that is always better than when the season is over
We are winning again and putting the pressure on them
That's what we like to do and we have to do it next week.
"Liverpool have a tough schedule with the Europa League and that's always difficult to keep the momentum in the Premier League
That's good because we are close but we need more wins, we know.
"I am very happy and still have one year on my contract
Everyone can be very happy how it works."
Long now has six goals in his last seven games against Villa but missed several chances to add to his tally, including hitting the bar early on.
And Koeman revealed the Republic of Ireland international said sorry afterwards for not scoring more.
He said: "He apologised after the game because he wasn't scoring more goals that one
It's a good mentality because he had some good possibilities to score
"He knows himself he had more opportunities to score and I like it
I never complain to a player who is working hard and doing everything
It's part of the job to miss chances
He was positive because he is working hard and creating a lot of problems."
Ashley Westwood's double was little consolation for Villa, who were constantly jeered by their own fans after gifting the Saints their first two goals.
Defeat was Villa's 10th straight league loss and they are a game away from equalling a club record run when they lost 11 matches in 1962-63.
Leandro Bacuna, Joleon Lescott, Brad Guzan and Micah Richards were prime targets for the boo boys but Villa caretaker manager Eric Black refused to criticise the fans
This week supporters have seen club captain Gabby Agbonlahor suspended as the club investigate alleged laughing gas use while it was revealed Jores Okore has effectively gone on strike by refusing to be on the bench against Bournemouth earlier this month
Black said: "It's difficult circumstances, they are trying to voice their opinions
We are professional people, professional footballers, and it's not always rosy in the garden
"I can only do what I do and try to improve them but we are not at the bottom of the league because we're the best team and have the best players
We have to keep working hard with them and they have to remain professional.
"I'm standing there so I'll take it (the abuse)
I understand the fans' frustrations and they have ideas on what team they want to see but I can't be led down that road.
"They've have had the worst season in recent history, they have seen poor results and performances
They have every right to voice their anger."
Source : PA