Inter were hammered 5-0 by PSG in the final, which saw coach Simone Inzaghi leave for Al-Hilal.
Barella said: “It’ll stay in our minds – it’s a loss that becomes a part of your journey in your career. It’s a tough defeat that stings but in life, as in football, you need to know how to get back up and we’ve shown we can do that.
“We lost two league titles by a single point and lost two Champions League finals but, in-between, we’ve also won.
"We know that football is full of highs and lows and you always have to keep working harder to reach the point where you can compete for trophies. That’s the mindset.”
On Inzaghi's departure, Barella also said: “It was a strange piece of news. After four years, being together had become the norm.
“At Cagliari I experienced many changes in coach and even a bit at Inter. I know how it works but I can’t say I’m used to it.
“The only thing I felt was the need to thank Inzaghi and his staff for four fantastic years – years of growth and strong emotions.”