"You know if you only score one goal they still have the belief," the Dutch manager told the club's website (www.saintsfc.co.uk).
The former Ajax and PSV Eindhoven manager said opponents West Ham were more aggressive and direct in the second half.
"It was one team on the pitch playing football, but we got what you can expect from them after half time," Koeman added.
Both teams came into the game about 48 hours after their Boxing Day fixtures. Koeman, who was critical about the fixture list earlier, said there was no issue on the physical side for his team.
"They scored two goals out of a better second half and we scored one goal out of a fantastic first half," he said. "That's the difference."
With Monday's loss Southampton have picked up only four points from their last seven league games, leaving the Saints in 12th spot on the table.
"... one of our problems is that if you are so dominant on the pitch and it's still 1-0 you give them the chance to come back," Koeman said.
"That we have to change, but it needs time."
Southampton's next match is against Norwich City on Saturday. The Canaries are in 15th place, four points behind the Saints.
(Reporting by Chris Peters in Bengaluru; editing by Sudipto Ganguly)
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