To me, it suggests that the speaker is a member of some group, and the article the implies that he didn't say anything to incriminate those in the rest of the group.
Omitting the article would make the sentence mean he was careful not to incriminate anyone. But when you say the others, it refers to some subset of people.
What group? It could be a gang of theives, a corporate board, members of a political party, members of his family, cosuspects in a case, codefendents in a lawsuit. The sentence only provides a pronoun – so, nobody knows what group it is! However, I'm confident that, with more information (who was talking, the nature of the questioning, etc.), I could figure it out.
For example, if the person was Lance Armstrong, and the sentence was uttered this week, I would surmise that the others might refer to fellow cyclists, probably on his team.