Nathaniel Clyne celebrated making his England debut recently with a thunderous equaliser late on at Villa Park on Monday after Gabby Agbonlahor had put the hosts ahead.
Southampton came into the game off the back of eight wins in their previous nine league games, but showed little of the attacking verve that has seen them mix it with the top-flight's leading lights.
However, with Manchester City, Arsenal and Manchester United to come in his side's next three games, Koeman is relishing the challenge to once again show Southampton mean business.
When asked if he was confident of a top-four finish, Koeman told Sky Sports: "Yes of course, but first we have to play better than we did.
"Everybody knows that the Premier League is a battle every game and there are big teams but they are struggling as well.
"If we keep going and keep our spirit like we showed - we had great character and we showed great patience in the second half - then I think it's possible because I don't see many teams better than Southampton.
"It's a nice week to play and we live game to game with three big teams.
"In this game Aston Villa had some key players injured, maybe [that made them] are more dangerous and it was difficult.
"We didn't reach the level we can reach and we must reach that to be competitive against City on Sunday."
