I disagree, completely. God wants your COMPLETE dependence on HIM. So, to ask for small things (like, the ability to be able to buy more tea this month) is just as important as big things (like my son is dying, will you help him?).
Personally, I am not too proud to ask God for anything. I talk to Him all day, not just in prayer at the beginning of my day. He is with me always, so I talk to him a LOT.
To think of God as "too busy" is to determine that He is not interested in YOU, and all the things YOU are. That would negate the description of "having a relationship". God wants a RELATIONSHIP, not your RELIGION. So, yes, He is interested in EVERYTHING about you.
Even if you just want some tea.