The Saints, who have placed eighth and seventh in their last two Premier League campaigns, have lost just once in their last six games
They lie in eighth place, three points behind Liverpool, who have a game in hand, and five adrift of West Ham
He said: "It is always possible (to get into Europe, but) we know it is very difficult because we know it is a gap of four or five points between us and Liverpool and West Ham
"That makes it difficult, but if you win the last four then you have a better chance.
"That is why we are still focused and concentrated on this Saturday (when Southampton travel to already-relegated Aston Villa), because it is still not the end of the season and I don't like to end the season in a bad way.
"There is progress in the team and with individuals in the team, but I do believe we lost some big opportunities in several games - mostly away from home
That is the question why there is a gap between the teams above us.
"It is possible, it is achievable, but not if we make mistakes like we did in some of the games or even most of them away from home
"We lost too many points and hadn't enough wins away from home and that makes it more difficult.
"It is not enough because the teams above us won their games and got many points and there is a gap.
"I already knew that after the draw against Everton (last weekend), because that was a really big opportunity that we missed not to score and to stay more close to the teams above us
Now it is really difficult, but still we need to believe to finish the season in a good way and that starts this Saturday."
A bad run of form from late November to early January, which saw Saints pick up just four points from a possible 24, looks to have cost Koeman's side
He added: "It is always difficult for teams like Southampton to play well all season and sometimes you need to come through a bad period
"We still have good games to play and this Saturday is a difficult one for several reasons
They (Villa) are already relegated, it will be a difficult atmosphere in the stadium.
"More than ever we need to focus on ourselves and take the motivation out of ourselves to play on a good level and win the game.
"I think we need more productivity in our final part attacking-wise, because the final pass isn't always a good one
(We need) to be more ruthless in the box."
Source : PA
Source: PA