Eddie Howe’s men appear to have turned a corner after back-to-back wins over West Ham and Swansea brought to an end their poor run of form.
Surman says the side must not repeat their finish to last season, when they won just two in 11 matches, if they are to retain their status in the top flight.
"Our job is not done. We have 33 points and that is not going to keep us up,W Surman told the Daily Echo.
"We are well aware our run-in last season was not great. We had some extremely tough games and we were in a different position, we already had 40 points."