Philippe Montanier's side were 2-1 victors over Malaga a fortnight ago and followed that up with a 4-0 demolition of Rayo Vallecano on Monday.
A win over Osasuna will see them rise to sixth, and Illarramendi has demanded concentration and that his team-mates don't listen to the hype around their recent showings.
"We can't go crazy with all the praise because in the last two games the team has played well. We had quite a bad run, but the last two wins have put us ninth. Now have a chance this Friday and we will hopefully win," said Illarramendi.
"We are doing well in the league and we must continue that streak. At home we are strong and we have to continue like this.
"Rayo came to play and is a team that gets a lot of goals, but Osasuna will play further back. We will have opportunities and I think that we'll get some goals."
Visiting coach Jose Luis Mendilibar says his side will be going all out for the win, knowing three points will see them climb out of the relegation zone.
"The important thing is to play the way we want," he told reporters. "Playing well we will have more chances to win.
"We're going out to win. We're not going to draw, but sometimes a point after the game is good."
It is an attitude replicated by midfielder Raoul Loe.
"Three points for the team could see us come out of the relegation places," he said.
"The team has more confidence than before, now everything seems easier.
"It is important to win and move onto 12 points."