The Pamplona side endured a tough campaign in 2012-13 and only avoided the drop by three points.
This season looks set to be just as tough, with a home defeat by Granada followed by another loss at Athletic Bilbao.
Osasuna will be hoping to get their first points of the season this weekend against Villarreal - a match boss Mendilibar is heading into with a relaxed mood.
"I think we've trained well and we have prepared the match to win," he said.
"We're prepared to be strong from the start. In our house if we give a little, our fans will give us more and we have to take advantage of that.
"There is no emergency. You have to add and understand that from outside it looks otherwise, but trust in us and we know we lack concentration moments to win."
By contrast to Osasuna, Villarreal have enjoyed the perfect start to life back in the top flight.
The Yellow Submarine have followed up promotion by beating Valladolid and Almeria in their opening games and are confident of extending that run at El Sadar.
"We know that they are needy and they were not going to make this easy," Villarreal manager Marcelino Garcia Toral said of Osasuna.
"We have started well, but remember Betis who won their first four and then spent 10 without winning.
"We have to play at the highest level if we want to win every game. Maybe other teams can win without being 100 per cent, but not us. We need that intensity is needed in category to add up."