Auxiliary Bishop Eamonn Walsh made the comments in an interview with Bloomberg news service on Friday.
The inquiry revealed that the Vatican and the Papal Nuncio in Dublin had ignored requests for information.
The Vatican said the requests had not come through "appropriate diplomatic channels."
However, Bishop Walsh told Bloomberg he was disappointed and surprised by the Vatican's attitude.
He said that the Vatican should have shown "courtesy and cooperation" and added, "If it were me, I would apologise."
He told the news service he was speaking in a personal capacity.
The Report of the Commission of Investigation into the Catholic Archdiocese of Dublin, which was published on Thursday, covered a period from 1975 to 2004.
It revealed a litany of child abuse by priests which had been covered-up by the church, on occasions senior police officers also colluded in the cover-up.
In the course of its work it asked for details of reports on abuse sent to the Vatican by the Dublin archdiocese in 2006.
The Vatican did not reply but told the Irish Foreign Affairs department the request "had not gone through appropriate diplomatic channels".
A request for information from the Papal Nuncio was also ignored.
In February 2007, the commission wrote to the Dublin-based Papal Nuncio asking him to forward all relevant documents in his possession.
It also requested that he confirm whether he had any such documents but the Papal Nuncio did not reply.
Earlier this year, the commission again failed to receive a reply after sending the Papal Nuncio extracts from its draft report which referred to him and his office, as it was required to do.
The Vatican told the Irish Times it "was a matter for the local church involved".
A senior Vatican spokesman said diplomatic practice required that outside requests made to the governance of the Vatican pass through diplomatic channels, in this case the Department of Foreign Affairs in Dublin and the Irish Embassy to the Holy See in Rome.
The leader of the Catholic Church in Ireland has said he is deeply sorry and ashamed by the abuse the report had revealed.
Cardinal Sean Brady also apologised for the way the church covered-up the crimes.
The commissioner of the Irish police, Fachtna Murphy, apologised for the police failure to protect victims.
Victims groups are now calling for a similar inquiry to take place in every diocese in Ireland.
However, Bishop Walsh has said he does not believe that should happen.
He said it would be better for the Church to use its "time, energy and money" to improve child protection measures.
No responsibility or liability shall attach itself to us or to the blogspot ‘Clerical Whispers’ for any or all of the articles placed here.
The placing of an article hereupon does not necessarily imply that we agree or accept the contents of the article as being necessarily factual in theology, dogma or otherwise.