Was this a lack of faith?

As I read this the thought occurred to me, was this a lack of faith on Paul's part?

Acts 28:17-20(NKJV)

And it came to pass after three days that Paul called the leaders of the Jews together. So when they had come together, he said to them: “Men and brethren, though I have done nothing against our people or the customs of our fathers, yet I was delivered as a prisoner from Jerusalem into the hands of the Romans, 

who, when they had examined me, wanted to let me go, because there was no cause for putting me to death. 

But when the Jews spoke against it, I was compelled to appeal to Caesar, not that I had anything of which to accuse my nation. 

For this reason therefore I have called for you, to see you and speak with you, because for the hope of Israel I am bound with this chain.”

A couple of thoughts.  The first one is why were you "compelled to appeal to Caesar"?  Did you trust Caesar more than God to protect you from death?  The other thought is if he hadn't appealed to Caesar, would he have ever made it to Rome to fulfill God's plan for him?  In other words, was Paul's appeal to Caesar actually the mechanism that God used to have His plan fulfilled?