Jesus told us not to worry in Matthew 6:25-34. He said the reason for that is that if God looks out for the little things, will He not also look out for you?
Can worry and faith happen at the same time? I think they can. Read the psalms and you find, at the same time, concern/worry and the cry to God for deliverance. That cry out to the One who can make things right is an act of faith in the midst of worry.
So where does worry come from? I don’t think it is a lack of faith as much as it is the difficulty to see and to know. We can’t see God working behind the scenes even when we know He is there. He may allow us to walk through hard things, seemingly impossible things, even if we know He is there. That concerns us…not that God isn’t there but what we may have to face. Consider Jesus in the garden – he was concerned but didn’t lack faith. His faith was demonstrated in His calling out to the Father for relief. He believed God heard and that God could act.
Worry is part of being finite. It is part of lacking omniscience and omnipotence. Worry and faith can work together. In fact, they often work together. So if you worry, don’t feel faithless…call out to God and wait on Him to answer – that is faith and worry at the same time. And over time you may find that you worry less and less and your faith grows more and more as you learn to anticipate the kinds of things God does when His children are hurting.
Like with anything, worry to the extreme can lack faith. But it doesn’t automatically mean we lack faith. Many people feel guilty over the second when they shouldn’t.