Absolutely. If Trump didn't speak up, it's another opportunity for Obama to destroy the USA and allies. Trump should speak about Obama's failures continually for the next 4 years. Because Obama isn't going to shut up, and because Obama blamed his predecessor for everything going wrong.
I imagine that's what we'll see. Whenever Obama opens his trap about how Trump sucks on whatever issue, Trump will hit him hard with an "Oh? What about when you screwed up XYZ?" It'll be glorious. Obama's not smart enough to keep up with him, and Trump can easily bypass the hostile media with such messages.