The Giallorossi were handed a mammoth assignment in Friday's draw for what is their first appearance in the competition's last eight in 10 years.
Barca, who have not reached the semi-finals since their 2014-15 triumph, are widely expected to continue the charge that saw them sweep aside Chelsea in the previous round.
Despite the prospect of a daunting trip to Camp Nou, an upbeat Di Francesco assured the Catalan giants are not the only ones pleased with the fixture.
"We're happy with the draw because we're proud to be in the quarter-finals," Di Francesco said on Saturday.
"We know we'll be up against one of the best teams in the world with the best player in the world, Messi.
"We'll approach the tie with a positive mindset. We knew we'd have to face a tough side in the quarter-finals. It's a tie both teams are looking forward to and we'll go into it with our feet on the ground."
10 - No Italian sides have ever won the 1st leg of a Champions League quarter final away from home so far (3D 7L). Threat. pic.twitter.com/dJriRqAZje— OptaPaolo (@OptaPaolo) March 16, 2018
"Every game is important but we're playing Crotone now. I've told my players to forget about Barcelona," he said.
"It's only natural that the lads can't wait to play that match but if we want to do well in the Champions League we first have to do well against Crotone and it's going to be difficult."