The Zebrette approach the match after playing three games in six days - beating AC Milan and sharing a goalless draw with Torino after facing Anzhi Makhachkala in the Europa League.
The Serbian keeper hailed centre back Andrea Coda following the stalemate in Turin, but is fully aware that his side can improve in a bid to claw their way up the table.
"Coda has done some wonderful work. I am very happy with his performance," Brkic told www.udinese.it.
"[The point against Torino] is a step further and we have to be happy, but not too much because we can do better.
"Now we have to focus on Genoa and on getting more points."
Udinese head coach Francesco Guidolin knows the glut of matches has taken its toll on his players.
He told Gazzetta.it: "I can not ask more from our players.
"I will say it again, for the teams playing in European competition it is difficult to always be at the top of your game. It is not easy."
Genoa approach the match having rescued a 1-1 home draw against Parma after getting back to winning ways against Lazio on Sunday.
Head coach Luigi De Canio wants his side to show more cutting edge up front against the Bianconeri after they struggled to convert their chances against Parma.
He said: "The team created many scoring chances but it we were not effective in front of goal.
"We were too unbalanced then we attacked but were too hasty at decisive moments."