Rubin stunned the holders with a 2-0 win at the Vicente Calderon last week and Atletico, who had won 21 successive home matches prior to that, know they will need to produce something special at Moscow's Luzhniki stadium on Thursday to overturn that deficit and avoid elimination.
Uruguay international Rodriguez is not giving the tie up for lost though, telling reporters: "We know that it's very tough. We had a very bad result, (but) we've worked very hard this week and hopefully we can get a good result.
"We're the current champions but we need to show that over there and give our all.
"We'll try to achieve the impossible and get through."
Atletico's problems heading into Thursday's match are partly of their own making following a nightmare first leg.
Rubin took a sixth-minute lead through Gokdeniz Karadeniz but the Russian side were then reduced to 10 men on the stroke of half-time when Roman Sharonov was dismissed.
However, not only did Atletico fail to use their numerical advantage to find an equaliser, they conceded a potentially decisive second goal in embarrassing circumstances deep into stoppage time.
Atletico goalkeeper Sergio Asenjo surprisingly ventured forward after the home side won a corner, but Rubin broke and Pablo Orbaiz was able to slot into an unguarded net.
Atletico coach Diego Simeone assumed responsibility for that gaff after the game, but the Primera Division high-flyers will be determined to leave a better impression on Thursday.
Rodriguez, who scored Atletico's final goal in their 3-0 league win at Real Valladolid on Sunday, said: "Without doubt there is the desire for revenge. We didn't expect the first-leg result, and we didn't deserve it.
"There's no other option now but to try and win and continue forward."
Rubin may be favourites but their former Spain international defender Orbaiz insists the Russian side are taking nothing for granted.
"The tie is still open," he told Spanish news agency Efe.
"It will be a tough and complicated game and Atletico still have a chance, they are a very strong team. They've always been a big club, but before they had more ups and downs. Now they are in good form."
If Atletico do manage to get through, they could meet domestic rivals Levante in the last 16, with the Valencia-based side boasting a 3-0 first-leg advantage over Olympiacos.