Cika wannan jumla: Cocu da Netherlands sun halarci Euro 2000 bayan sun cancanci cancanta a matsayin mai masaukin baki. Kungiyar ta Dutch, tare da Cocu a duk wasannin, ta lashe dukkan wasannin rukuni da wasan kusa da na karshe da Yugoslavia. Duk da haka, Cocu da tawagar sun sake fitar da su bayan bugun fanareti a wasan kusa da na karshe, a wannan karon a kan Italiya. Netherlands da Cocu sun kasa cancanci zuwa gasar cin kofin duniya ta 2002 a cikin rukunin cancanta tare da Fotigal da Jamhuriyar Ireland. A shekara ta 2003, Cocu ya karbi wasansa na farko na kasa da kasa a wasan sada zumunta da Belgium. Netherlands ta yi kyau a wasannin neman shiga gasar Euro 2004, tare da Cocu ya ci kwallaye biyu (duka biyun a wasanni daban-daban da Austria). A lokacin
Euro 2004, an zabi Cocu a matsayin kyaftin din kungiyar kuma ya bayyana a dukkan wasannin. A wasan kusa da na kusa da na karshe da Sweden, ya rasa hukuncin kisa a cikin harbi, amma duk da haka Netherlands ta yi nasara. A wasan kusa da na karshe, an fitar da kungiyar daga Portugal mai masaukin baki. Bayan Euro 2004, Cocu ya rasa matsayin kyaftin ga Edgar Davids, shawarar da sabon kocin Marco van Basten ya yanke.