Walter Mazzarri's men head into the game unbeaten in six Serie A matches and still retain slim hope of gaining qualification for the UEFA Champions League.
Inter are 11 points behind Napoli, who currently occupy the final Champions League qualification berth and welcome fourth-placed Fiorentina to Stadio San Paolo this weekend.
A place in next season's UEFA Europa League, courtesy of finishing fourth or fifth, appears a much more realistic aim for Inter.
And with sixth-placed Parma only one point behind the 18-time Italian champions, Palacio knows it is vital his side claim three points against an Atalanta outfit seeking a fourth consecutive win.
"You can see the team has improved. Our understanding is growing just as the team is improving," Palacio told Inter's official website.
"It's becoming stronger and we have to keep this up. You only need to look at the results on the pitch and the recent performances.
"We can't fail on Sunday. We're playing at home and we have to win. We know Atalanta are a team that's tough to face. We'll need to be careful.
"We know we lost points in games we should have got something from, but we have to keep going the way we are now."
Inter will again be without suspended defender Juan Jesus, while Yohan Benalouane is banned for Atalanta.
The visitors have moved well clear of any potential relegation danger as a result of their recent upturn in form and will have designs on securing a top-half finish.
Stefano Colantuono's men currently sit ninth and can also take heart from their recent performances against Inter, who have not beaten Atalanta since 2010.
Atalanta completed a double over Inter last season with enthralling 3-2 and 4-3 wins, and held Mazzarri's men to a 1-1 draw in this season's reverse fixture in October.
Striker German Denis is likely to be key if Atalanta are to claim another success against Inter, having found the net 10 times this season and on six occasions in the last three games between the two sides.
Midfielder Maxi Moralez is confident Atalanta can emerge triumphant again and extend their unbeaten run against Inter, which currently stands at five matches.
Moralez told his club's official website: "We expect a tough match against Inter, an opponent with many champions and who are in shape.
"But we are also having a great moment and we want to keep going to the end of the season, in the best way possible."
