Popper did not do anything of the sort.

First, I think Popper did not fundamentally disagree with the Bayesian approach: ultimately his critique of Bayesianism is a small adjustment to Bayesianism. When presented with a set of competing hypotheses { h_0, h_1, h_2... }, Bayesianism says that we assign a probability to each, whereas Popper points out that experiments and observation never really actually add credence to a hypothesis, they rather only decrease the probability of a hypothesis.

In theory, decreasing the probability of hypothesis h_0 does not increase the probability of hypothesis h_1, because the set of hypotheses is infinite--that is to say for any n there is always a potential h_{n+1} which has not been thought of by scientists. We know that the sum of the probabilities of hypotheses must be 1, but since the set of hypotheses is an infinite set, decreasing the probability of h_0 does not necessarily increase the probability of h_1, because the probability of any h_n in the set could be increasing.

I think Popper is right in theory, but in practice, I think this is less important than philosophers think it is. Pragmatically, we can treat the set of hypotheses as finite, operating only on the hypotheses humans have... hypothesized. We have no way to operate on hypotheses nobody has thought of, so we just operate on the set of hypotheses we have thought of. Since the sum of this set of probabilities must be 1, decreasing the probability of one hypothesis does increase the probability of all the other hypotheses in the set. Where Popper's critique becomes important is if we keep decreasing the probabilities of all the hypotheses in the set--this indicates that the hypothesis which is true is not in the set (i.e. nobody has come up with the correct hypothesis to test). This indicates a need for new hypotheses. But in a lot of cases, experimentation keeps decreasing the probability of all the hypotheses except one in the finite set of hypotheses humans have thought of, while numerous attempts to decrease the probability of that one hypothesis fail. While Popper would say this does not increase the probability of that one hypothesis, operating as if it does increase the probability of that hypothesis seems to work. We've been able to go to the moon, eradicate smallpox, and build intelligent-seeming machines, all based on hypotheses that we "increased the probability of" in this way, even though increasing the probability of a hypothesis is theoretically impossible.

This all goes back to philosophers' favorite navelgazing claim: that nothing is knowable. Ultimately, I think this is a dishonest argument which even philosophers don't believe. I've offered to punch many a philosopher in the face: after all, it's not knowable that it's going to hurt. But strangely, philosophers who claim to believe that nothing is knowable DO seem to know that will hurt, and none have taken me up on my offer.*

* Unlike the philosophers, I do believe in (probablistic) knowability, and I'm highly confident that punching them in the face would hurt them, so if anyone actually takes me up on this offer, I (probably) won't punch them. So far, no one has called my bluff.