Can one define a "particle" as space-localized object in quantum field theory?

In Peskin and Schroeder, while discussing creation and annihilation operators for a Klein-Gordon field (p.22), the authors say, as we all know the creation operator $a_p^{\dagger}$ acts on vacuum to produce a state with momentum $p$ having energy equal to $\sqrt{p^2+m^2}$. Then they state: "It is quite natural to call these excitations particles, since they are discrete entities that have the proper relativistic energy-momentum relation. (By a particle we do not mean something that must be localized in space; the creation operator creates particles in momentum eigenstates)"

This clashes with my previous conception of a particle to be something localized in space; a point particle located at point $(x,y,z)$ for example, or an extended massive object occupying certain region in space. Form above should I conclude that no such concept of space-localized point-particle exists in quantum field theory? I am not familiar with the process of visualizing something in coordinate space which is known to be localized in momentum space. Please help.