Christian Norgaard gave the home side the lead from a free-kick midway through the first half before Liverpool’s Swedish international winger Kristoffer Peterson levelled early in the second half.
But Ferhan Hasani hit the Brondby winner in stoppage time.
Liverpool manager Brendan Rodgers shrugged off the loss in the team’s first game since Suarez’s EUR95 million ($128 million) move to Barcelona, preferring to concentrate on the challenges of the new Premier League season which starts on August 16.
“This year, we know it’s going to be extremely competitive. Every team will strengthen and we’ll be exactly the same. But the beauty for us is that we’re a young group and we’re bringing in young players that are hungry,” said Rodgers.
“We will progress again from last season. It’s going to be a really exciting season. I’ve seen development in the players already in the short period of time that we’ve been back. This season we have the belief to go along with the quality.
“We want to improve and continually improve. We’re working very hard behind the scenes, as we always do, in terms of getting the best quality players into the club.”
Chelsea defeated fourth-tier Wycombe Wanderers 5-0 with Patrick Bamford, Izzy Brown (2), John Terry and Branislav Ivanovic on the scoresheet.
In Austria, Crystal Palace enjoyed a 13-1 romp at GAK Graz with Stephen Dobbie grabbing four goals and Glenn Murray, Joe Ledley and Jonathan Williams all netting twice twice.
Yannick Bolasie, Jerome Thomas and Marouane Chamakh finished off the rout.