Have you been in situations in a new company or role, where you needed to assess the current technical debt, but did not want to appear to be critical of your predecessor? How did you navigate this?

I navigate it by doing the routine "Health Check and Assessment" of processes, tech, people, and strategy.

"Technical debt" is unfortunately a loaded term.  Without specifics, it's possible that there are compelling reasons for the existing infrastructure and level of maturity.  These investments may have served the organization well and generated positive ROI over time. 

I might phrase it as "we have existing technologies that we have wrung considerable value from over time; however, these technologies have reached an end of life and opened up an opportunity for us to invest in newer approaches."

I find the key is to get the teams to recognize that there are better ways to achieve an outcome and focus on that outcome.  WRT to starting the change I use an analogy that my car from 2010 is great, but that cars from 2020 are just better!  That doesn't mean that my car from 2010 is bad, only that technology/comfort/safety all made huge leaps forward in the 10 year period and we need to take advantage of the new situation.

I try to separate the problems from the predecessor.  Focus on fixing the problem, not casting blame.  I also try to find opportunities to praise staff who carried over from the prior leader, when it's appropriate.

This can be tricky to navigate. You need to focus on the issues, not the people. 
Since you are new, treat it like an opportunity for a fresh start and to help realign with best practice. Provide the team blueprints, and best practice guidance and ask them to do a gap analysis. They will see the issues, and it becomes about uplifting the capability, not about the person that made previous decisions. 
You will still need to ask 'why' things are the way they are in case there is a legacy system hiding in there that you can't update for one reason or another, but it is still about the systems, not the predecessor. 
Get the team thinking about how to upgrade or update the systems, and be their champion, then it won't matter what your predecessor did providing you can put together a roadmap to bring the IT landscape up to current.