Inter's hopes of securing a top-three place in Serie A hit a major snag when the 33-year-old striker suffered season-ending ligament damage in Thursday's Europa League victory over Cluj.
Cambiasso, however, feels his team-mates have been given extra incentive to chase Lazio out of third place - a mission that continues at Fiorentina on Sunday night.
"We just have to think about the games ahead of us," Cambiasso told inter.it. "But what happened to my team-mate, who is also my friend and my brother, does hurt. We all feel his pain.
"It's normal that he's disappointed and it's not a straightforward injury, but I am calm because he know much he wants to get through it.
"We now have an even greater responsibility to earn our friend the Champions League football that he deserves. We are always trying to go above and beyond.
"But we need continuity before we can start talking about 'the real Inter'. We need to fight to achieve the goals we initially set ourselves and we can only do that through finding continuity in our performances."
Next Sunday sees Inter bid to do the double over city rivals AC Milan in the second Derby della Madonnina of the season.
Cambiasso is urging caution, though, with an energy-sapping trip to Romania calling shortly after Sunday's exertions in Tuscany.
He added: "There are two games before the derby. It's a long way off even if the fans think it is close. It may be our next home game, but we're taking each game as it comes."
Fiorentina also started the season with European ambitions but Vincenzo Montella's men have slipped down to sixth place having picked up only four points from six games.
La Viola should be boosted by the inclusion of Mohamed Sissoko, who could make a delayed debut after helping Mali to third place at the African Nations Cup.
The on-loan Paris St Germain midfielder said: "I liked what the club had to say. I wanted to get back to playing and so I decided to come and play for Fiorentina.
"The club convinced me right away. I'm not yet 100 per cent fit but I feel ready to play.
"The plan is to get into the Champions League and I think we can do it. I will give my all to help us get there."