The EC statement followed comments from Prime Minister Anthony Albanese that any deal would need to give Australian farmers' goods, especially beef and sheep meat, more access to the bloc.
"We won't just sign up to a deal for the sake of it, what we want is a good deal for Australia," Mr Albanese said on Tuesday while visiting Lithuania.
"We regret it was not possible to conclude our talks with Australia this week," an EC representative said on Tuesday.
"We made progress but more work is required to address key outstanding issues," the representative said.
Trade Minister Don Farrell said officials on both sides would continue negotiations and try to meet again next month.
"As we've said all along, Australia needs meaningful agricultural access to European markets," he told reporters in an impromptu press conference in a park in central Brussels.
"I'm optimistic that with some goodwill, some hard work, some perseverance, we're going to get there," Mr Farrell said.
Mr Albanese discussed the idea of an EU free trade agreement (FTA) with French President Emmanuel Macron on the sidelines of the NATO summit in the Lithuanian capital Vilnius on Wednesday.
National Farmers' Federation chief executive Tony Mahar, who is in Brussels, said agriculture was always one of the final issues to be resolved in trade negotiations.
"That's proven the case with this one, it's challenging," he told the ABC.
"Trade is critically important to Australian agriculture."
Mr Mahar said if the offer presented by the Europeans wasn't good enough, the government should walk away before trying to strike a deal again later.
"It's too important not to get it right... we want to make sure that we get this right for Australian farmers from the first day for the decades that follow," he told the ABC.
A sticking point in the trade talks is the EU's objection to Australian food producers using terms such as feta and prosecco.
Australian negotiators argue it is reasonable for farmers to use the terms to represent varieties rather than European regions.
Opposition trade spokesman Kevin Hogan said he agreed with the idea of walking away if farmers were not offered adequate access to the EU market.
"We shouldn't rush this deal if it's a bad deal for Australia," he told AAP.
Mr Hogan doesn't want to see "'grandfathering" of geographical indicators where only existing producers could use names such as prosecco and feta.
"The European Union is a big economy, there's a lot of customers there for us, but we certainly don't want to do that at any cost," he said.
"A deal can be done but we shouldn't blink before the Europeans do."
with Reuters
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