Manolo Jimenez's side have pulled clear of the relegation zone after getting seven points from their last three games, after failing to win any games in La Liga between the turn of the year and April 27.
For the last three years they have avoided relegation thanks to picking up points towards the end of the season, and during the week the former Deportivo La Coruna and Villarreal coach Miguel Angel Lotina remarked that it was "curious" that Zaragoza always won games in the final stretch of the season.
In a press conference Apono vehemently denied the accusations, declaring:
"They are trying to distract us, make us nervous and make us think about things we shouldn't be thinking about. We have to just focus on the next game. All this goes in one ear and out the other.
"I didn't feel the accusations were aimed at me, because I have always played to win," he added. "It's another thing if people try and bribe me, but this has never happened to me and I hope that this never happens to any team I am at."
Apono insisted the team was just focusing on their game with Athletic Bilbao at La Romareda, in which they can take another step towards survival.
"It's going to be a fantastic game to play in and we need to get the three points so we don't get dragged back into the bottom. If we win we will be very close to our objective.
"We have to win because we are just two points above Deportivo. If they lose, we could go five points above them. We have had three very good performances and as we were capable of that, we have a very good chance of beating Athletic. But we also have to control our nerves, if we don't, we won't get anywhere."
The midfielder also had words of gratitude for the club's fans who he said "have proved that they are behind the team".
"They have given everything to support us and this turnaround also belongs to them," he added.
Athletic Bilbao will guarantee survival if they get a point from the game with Zaragoza, but could even be mathematically safe before kick off, if Deportivo fail to beat Espanyol.
Marcelo Bielsa's side will be without injured centre-back Borja Ekiza and full-back Andoni Iraola, who is suspended.