Roma are six points behind the Nerazzurri following their 4-1 win against Palermo on Saturday night.
Brighi scored two of the goals for Roma in the game.
“We are progressing well and we want to aim as high as we can, but it was a tough game for us tonight,” Brighi told Sky Sport Italia after the game.
“We were able to play really well though and we obtained maximum points.
“Inter? It’s clear we are behind them, they are a great team, but they have to lose points for us to catch them. We will continue to do our work.
“We feel we can continue doing well and it’s right to keep trying until the end.”