Southampton sit fourth in the English top flight, two points clear of fifth-placed Tottenham, following their 2-0 win over Arsenal at St Mary's Stadium on New Year's Day.
That result, secured by goals from Sadio Mane and Dusan Tadic, came on the back of a 1-1 home draw with title challengers Chelsea.
Attention now turns to Sunday's FA Cup tie with Championship side Ipswich Town, but Koeman thinks his side have the confidence to challenge for a UEFA Champions League qualification place.
"It's difficult to be always on the top. We are back in our way how we like to play football," Koeman said. "The confidence in the team is back after the draw against Chelsea. Yesterday [Thursday] was another example that we can beat teams like Arsenal.
"Sometimes you watch the table, that's normal. Little by little, we believe in our qualities and a top finish in the league.
"We have to be in every game 100 per cent and keep the spirit in the team. If we can keep that, everything is possible."
Mane limped off in the 42nd minute of the victory against Arsenal with an apparent hamstring injury, leaving Southampton facing an anxious wait over the results of a scan the Senegal attacking midfielder will undergo on Friday.
Koeman added: "We have to wait for the results of the scan, and then we can say something more."
