The Liverpool player has moved to the Reebok Stadium on a season-long loan, but was unable to prevent the Trotters from losing 3-1 at Hull on his debut.
Owen Coyle's side sit 20th in the npower Championship table after their four opening games, and the midfielder, 23, says the players must take responsibility.
Spearing told Bolton News: "If we get our heads together and stop making silly mistakes, I think we will be right up there.
"The players we have got here are more than capable of beating teams like Hull and anyone else in this league. We really do need to get as many points as possible.
"It was just individual errors that caused us problems and we have to stop those straight away if we want to be near the top."