I was in the interview process for SFA role for a big tech company. Made it to the final round. However, after the final round, I got a rejection email. They were nice to provide a feedback.

In general, the team liked my skills (very relevant experience, strong analytical skills, open for a feedback, detail-oriented, etc.). Crushed their technical assessment. However, what made them reject my candidacy is a weaker verbal communication compared to other candidates.

I performed poorly on that because was too nervous as it was the final round (I had to talk about past projects).

My question is how significant is verbal communication vs. other skills? Can you really get rejected due to bad verbal skills? How do I improve it?