In a press conference in Brussels, European Council President Charles Michel warned that UK access to EU markets would be more restricted once it has left.
"The more the UK will diverge from the EU standards, the less access to the single market it will have," he said.
Commission president Ursula von der Leyen said relations with the UK would never be as close once it is outside the EU.
"We want to have the best possible relationship with the United Kingdom but it will never be as good as membership," she said.
She quoted Jean Monnet, considered to be one of the founding fathers of the EU, saying: "We are not optimistic, we are not pessimistic, we are determined."
Earlier, Ms von der Leyen told the BBC: "It is a very emotional day. Negotiations will be fair.
"But, of course, each side will fight for their interests.
"And it is very clear that there are some fields where we have strong common interests.
"For example, the fight against climate change."
She added: "You know it is the story of old friends and new beginnings now.
"Of course, we want to work together as close as possible. The crucial part is the single market.
"And there, there is a clear trade-off - the closer the UK wants to be to the single market, the more they have to respect the rules of the single market.
"If they do not want to respect the rules and the standards of the single market, the more distant, of course, they will be.”
The UK Government also signalled that trade talks would result in a more distant relationship with the EU.
Chancellor of the Duchy of Lancaster Michael Gove told the BBC that the UK was “moving further away from the orbit of EU rules and laws”.