It follows a clash with head judge Shirley Ballas on last weekend's live show.
Speaking on It Takes Two tonight, Brendan admitted that "emotions were high" after he and celeb partner Charlotte Hawkins completed their latest dance.
"For the people out there that I've offended by having an opinion on what we did out there, we've got to make this about Charlotte and what she is doing on the show," he told host Zoe Ball.
Speaking on Thursday night's edition of the BBC Two spin-off, Brendan went on: "[Charlotte] did such a good job on Saturday, and I was really disappointed not to have a bit more positive feedback for her so going into the week, we can [see] that we've made progress and are going to keep on making progress.
"Your emotions are high. You do tend to get [emotional]... This week, we're going to have some masking tape ready. I will not say anything. This is my promise to Charlotte and the nation!"
Charlotte quipped: "I've been training him to zip it."
Last weekend saw Brendan and Charlotte dancing the Tango to Danger Zone from Top Gun, before a clash between Brendan and Shirley.
In the comments, Shirley complained about the rise and fall in the routine but Brendan claimed she was "wrong".
Bruno Tonioli also got involved, telling Brendan: "I think Shirley is right and I feel you should be more respectful."
Strictly Come Dancing 2017 airs this Saturday and Sunday night on BBC One.