After drawing 2-2 at home to Ajax in their last outing, the English champions have no room for error and must beat Jose Mourinho's side at the Etihad Stadium to stand any chance of reaching the last 16.
Even then, the odds would be stacked against them.
Only two teams have previously qualified from such a hopeless position after four group matches -- Lokomotiv Moscow in 2002 and Porto in 2004 -- and City would still need to win at Borussia Dortmund in their final group game and hope other results went their way.
Aguero, who netted twice in City's 5-0 defeat of Aston Villa at the weekend, never won against Madrid during his time with their city rivals, Atletico, but he hopes Wednesday's game will bring that jinx to an end.
"We should never give up. Where there's a will, there's a way, right?" the Argentine told City's official website.
"Of course, it's harder now because we're not just relying on ourselves but also on the other teams' results.
"I think it's even more significant now than if we had been in a better position in the table. It may sound strange but I firmly believe that. We must win this game.
"We have a great team, I have no doubt about it and now it is time for us to show just how good we are."
City coach Roberto Mancini declared his side's chances of reaching the knockout phase dead after the draw with Ajax left City bottom of Group D with only two points, but the win over Villa -- which took City top in the Premier League -- softened his tone, albeit slightly.
"We want to do a good job. We will have not much of a chance to go through, but we will try," said the Italian, whose side lost 3-2 in Madrid in their opening group fixture after conceding a 2-1 lead.
In Mourinho, Mancini faces the man who succeeded him as coach of Inter Milan in 2008 and then led the Nerazzurri to the Champions League title two years later.
It will be Mourinho's 100th match in the Champions League and at 49, he has reached the milestone at a younger age than any other coach.
A popular figure in England since his three-year tenure at Chelsea, Mourinho returns to the country knowing that defeat at Mancini's hands could seriously compromise Madrid's season.
The Spanish champions are already eight points behind Barcelona in La Liga -- a potentially insurmountable gap -- and the pursuit of the club's 10th European Cup ('la Decima') has therefore been given added significance.
Cristiano Ronaldo will return to play in Manchester for the first time since leaving Manchester United in 2009 and can therefore expect a noisy reception from the fans of their cross-town rivals.
The Portuguese forward's future is the subject of speculation, amid reports he is seeking an improved contract, but he was still acclaimed by the club's fans during Saturday's 5-1 demolition of Athletic Bilbao.
Sami Khedira, who netted the fifth goal against the Basque side, says Madrid should look to follow the pro-active strategy adopted by Dortmund when they held City to a 1-1 draw in October.
"Dortmund showed how you can compete there: playing a tight game, competing for every ball, and trying to impose your style of play, so I think we have a good chance," the German midfielder told the club website.
"But we definitely have to concentrate on trying to play our own way there, not letting ourselves be influenced by the opponent's style, but instead imposing our strength in attack."
Both teams have problems at left-back, with Marcelo (broken foot) out for Madrid and Gael Clichy (ankle) a doubt for City.