A connecting structure and method for affixing an open end of a tube composed from thermoplastic resin material(s) to a tube connecting portion of a quick connector having a cylindrical geometry and at least one annular stopper on the cylindrical outer circumference thereof with said tube connecting portion being adapted to be press fitted into said open end of said resin tube. The connecting structure comprises; an annular band composed of elastomeric rubber which surrounds the open end of said resin tube adjacent the location of attachment to said quick connector having a length at least equal to the diameter of the cylindrical outer circumference of the quick connector and a diameter such that a tightening force is applied to the resin tube upon press fitting said tube connecting portion into the open end of said resin tube to prevent disengagement therefrom. The connecting structure forms an integrated assembly with the tube connecting portion of the quick connector.