"Our job is not done. We have 33 points and that is not going to keep us up," 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.
"It is a little bit different this season. We need the points but this is a great start and now, hopefully, we can start looking up rather than down."
Eddie Howe's side, who won consecutive league games for the first time this season, visit 10th-placed Southampton on April 1 before facing fourth-placed Liverpool at Anfield on April 5.
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(Reporting by Hardik Vyas in Bengaluru)
