Speaking in Parliament on Thursday, the Irish official said this was vital in helping to restore public trust in the EU generally.
She said one step could be publishing key documents related to trilogues.
These documents include trilogue dates and summary agendas, the positions of co-legislators on the Commission's proposal and the names of the decision-makers present in trilogue meetings.
Documents that track the main stages of the process should be published as soon as possible after the negotiations end, she said.
O'Reilly said that unless there was an improvement in transparency, particularly at Council level, the "corrosive caricature of faceless Brussels eurocrats" will increase.
She told a hearing, "This, in turn, will do further damage to the legitimacy of the EU."
The official, who investigates maladministration at EU level, was a keynote speaker at a public hearing on "restoring citizens' confidence and trust in the European project."
O'Reilly said it had been too easy to blame the EU for Europe's economic malaise in the past, adding that member states should accept more responsibility for a communications failure in getting the EU's message across to citizens.
She said, "My job is to encourage the EU to be more open but it is also up to member states to help raise awareness of the European project."
O'Reilly also referred to the EU's much vaunted ills, saying, "Until recently, it has been too easy to talk of this as an existential crisis for the EU but, while eurosceptic parties have certainly had some influence on domestic politics, what we have seen recently is that the EU is actually holding together.
"The mandate for a hard Brexit Theresa May sought in the election did not materialise, the surge in support for euroscptic parties has been stemmed in elections in the Netherlands and, on his election night, Emmanuel Macron marched to the tune of Ode to Joy, the EU anthem."
She also felt that recent events such as Brexit and, in the United States, the lessons learnt by the election of Donald Trump had strengthened, rather than weakened, the EU project.
This, she said, was because the public were now slowly becoming aware of the complexities and difficulties caused by Brexit and the outcome of the EU referendum which, added O'Reilly, had taken place "against a backdrop of soundbites."
The EU may still be set to undergo significant change, she said, adding, "but if change is in the air everyone must put the needs of citizens first. People want to be treated as citizens, not customers, and they should be the primary focus."
Her comments were largely echoed by Slovakian MEP Pál Csáky, a Vice- Chair of the petitions committee, who noted that earlier in the week the committee had heard five hours of evidence from the public, mostly Britons, concerned about the possible negative impact on their rights by the UK exiting the EU.
Csáky, who opened the debate, said, "I think it was very impressive to see this representation. It shows that many British people still want to retain cooperation with the EU and also keep EU citizenship."
He added, "This, to me, suggests there is such a thing as a European identity and that is something that unites us."
In March, the ombudsman decided to look into how European law is made in the Council, a practice branded as a "black hole" by NGOs. As part of her investigation, O'Reilly asked the Council to clarify how documents from the various meetings of national civil servants and ambassadors are handled in accordance with EU transparency standards.
She said she wanted to know when and how the positions of individual countries on draft laws are recorded and how Council has implemented a 2013 European Court of Justice ruling on transparency. She also asked how the Council decides on which documents should be classified as 'LIMITE', the lowest level of secrecy classification.