Allardyce recorded his first win in charge with an FA Cup replay victory against Bolton in midweek and Koeman said: "I think with his experience he is the right man in the right position.
"It's always difficult for a new manager coming to a new place during the season. You need time, maybe they are struggling a little bit but they still have good players, they still are physically a strong team, they're strong at home.
"I think it was really important for them to win the game last Tuesday against Bolton and we will see. We can't celebrate what we did last week because you know in football you have to prepare yourself for the next, and the next maybe is still more difficult than it was last weekend."