The Nerazzurri are currently six points behind Lazio in the race for the third and final spot for Europe's most prestigious club competition with only six games to go.
Andrea Stramaccioni's men travel to Udinese on Saturday, who are also looking to qualify for the Champions League, but Branca admitted that Inter's chances of reaching third place look slim.
"In all honesty, I don’t think we are in the race for the Champions League. All I can say is that we will do our best to the bitter end," confessed the technical director to Udinese Channel.
The former forward then spoke of the Zebrette, who he made over 120 appearances for during his playing career.
"I think the Friuli fans are very fortunate to have the Pozzo family at the helm. They started with me in the 1987 team and escalated with a mix between young and experienced players to reach great results," he stated.
"I am always glad to come back to the stadium I played in for five years and was very happy here. Even if I know this will be a complicated game for Inter, it’s still a pleasure to be here."