Think in layman terms - you have fixed amount of money, you have 2 options to spend it on both at time t=0 offer same returns, then at t =1, central bank steps in and tips the scale in favour of depositin money with the bank by raising the rewards you get for it (Interest Rate).
This would imply that you’d be biased to save than spend, i.e. less demand for products, which translates to a decline in aggregate price levels.
another way of looking at it, if you’re more of a visual learner like myself and like drawing S/D curves quickly for these questions, an increase in bank reserves leads to a leftward shift of both LM curve, and AD curve. which makes sense intuitively as well - that is, when the cost of borrowing is very high (b/c the interest rates went up), consumption and investment (C + I) will suffer, shifting the AD curve to left. a leftward shift in demand for goods, will definitely not drive prices up, but if anything induce price cuts.