The laws, under which all asylum seekers arriving by boat would have been processed offshore, passed the Lower House last week but faced defeat in the Senate.
Mr Howard, says he is disappointed the Bill will not go ahead, but it could not succeed.
"What has happened is that the Labor Party and a small number of coalition members and senators have together - not acting together, let me make that clear - but their views have virtually coincided that combination means we would not secure passage of the legislation," he said.
Mr Howard said there was no point having a protracted debate when the outcome was already known.