An Argument Against Karl Popper's Alternative to Induction

The great twentieth-century epistemologist, Karl Popper, did a lot to contribute to the philosophy of science.  There is a highly intuitive nature to what he suggests about the scientific method, or rather what the scientific method ought to be.  In short, he says that whenever one scientific theory t1 is able to explain a1 but not a2, then some new theory t2 must supersede t1.  Moreover, t2 must be able to explain a1 just as well as t1 did in addition to explaining a2.  For instance, Newtonian physics explains various motions and gravitational constants under a certain paradigm ("paradigm" is a phrase used by Thomas Kuhn).  However, it does not explain all of the data, and it ended up being superseded by Einsteinian physics.  This, in turn, may also be superseded by an additional theory t3, e.g. a theory of everything that attempts to unify Einsteinian physics with quantum mechanics.

So far so good.  However, it's peculiar that Popper rejects the principle of induction and suggests that what was explained above constitutes an alternative.  After all, if the principle of induction is dispensable, then we cannot assume the future is going to be like the past.  However, this means that there is no guarantee that any additional theory will be needed.  Science, with respect to the limitations of science, could for all we know end up being exhaustive.  Only by assuming the principle of induction is indispensable can we make the claim that future data will need additional explanation.  Therefore, it stands to reason that Popper's rejection of induction is self-defeating.