We show that depositor inattention gives banks deposit market power, explaining incomplete monetary pass-through and generating interest rate exposure that changes sign over the monetary cycle. We present a dynamic deposit-pricing model in which banks trade off current deposit spreads against future deposit base, with inattention dampening spread-sensitive outflows. Empirically, we measure inattention using differential responses to scheduled versus unscheduled income and show that inattentive depositors withdraw less following rate hikes. The data confirm that banks with more inattentive depositors have lower deposit rates, weaker pass-through, and less spread-sensitive outflows. Our calibration quantifies how inattention shapes pass-through and financial stability.