This verse is part of the longer version of Tachanun recited on Mondays and Thursdays. The Talmud in Brachos (7b) explains that Daniel was only saved from the lions’ den because of the merit of Abraham. He did not ask G-d to act “for Your sake,” but “for my Master’s sake.” He was asking for protection in the merit of our ancestor Abraham, who called G-d by this name (Genesis 18:3).