Before flying to San Jose on Thursday in preparation for Game 3 at SAP Center on Saturday (8 p.m. ET; NBCSN, CBC, TVA Sports), Sullivan said he would not entertain Couture's remarks before commenting briefly.
"I have no response to it," Sullivan said. "My main concern is about our hockey team and our mindset, our determination and the focus of our group. That's where my main concern is and that's where I'm going to use all my energy."
Sharks coach Peter DeBoer also chose to avoid comment upon returning to San Jose.
"I'm not going to weigh in on that," DeBoer said.
Neither Crosby nor Couture was available for comment Thursday.
Sullivan said he is not worried Couture's comments could affect the enforcement of faceoffs moving forward in the series.
"I'm not concerned at all," Sullivan said. "All centers, when they're taking faceoffs, they're trying to get an edge. That's just the reality of it. They're doing the same thing that our guys are doing. The way I look at it, that's all part of being a center-iceman and trying to figure out ways to get an edge and be successful. So, Sid's not doing anything that their guys aren't doing.
"Quite honestly, it really isn't worthy of a response. So, as I said before, my main focus is on our group and on our mindset going into this Game 3. We want to make sure we focus on the task at hand."