This sentence below depends on what you want to say:
I thought you needed to say something, but it seemed you had chickened out.
"I thought" in the past, preceded by something farther back in the past, such as something occurring before the moment the meeting took place.
COMPARE that to:
I thought you needed to say something, but it seemed you chickened out.
The chickening out and the "I thought" basically occurred at the same time, when the meeting took place.
Please note: The timeline issues with verb tenses are not only a matter of grammar. They are also conditioned by what a speaker wants to say and means to say about a situation that we, those who answer these questions, cannot determine. ELLers seem to have difficulty grasping that their actual intentions in saying something can be as important as the grammar.
1) I thought you needed to say something, but it seemed you had chickened out. [at that point in time]
2) I thought you needed to say something, but it seemed you have chickened out. [at this point in time]
3) I thought you needed to say something, but it seemed you chickened out. [then]
All three are valid, all three say something different about the reality of chickening out and the meeeting.