The La Liga giants face three league champions – Paris Saint-Germain (Ligue 1), Ajax (Eredivisie) and APOEL (Cypriot First Division) – in Group F.
Mestre said Barca had been handed a tough draw, even wary of arguably the group's weakest team – APOEL.
"For me, it's a difficult group," he said.
"PSG are a tough team. Ajax we played last season and are tough as well. APOEL in the beginning could be an easy team, but we don't trust in that kind of thing."
PSG president Nasser Al-Khelaifi said he had the utmost respect for Barcelona and Ajax.
"We are also a great club this season I think," he said.
"I respect Barcelona a lot obviously. That's a great club, they've won it four times. Do not forget Ajax, they've won it four times.
"We respect them as a football club. We will try to win all our games and get the three points, always."
'I don’t get any respect. I’m not going to kiss someone’s ass to be loved - what is the problem with wanting to win prizes? If someone else does that, there is no problem' Romelu Lukaku laments media treatment during Premier League days
Bayern Munich make final decision on former Erik ten Hag favourite: report
