Aguero struck twice in the last five minutes to complete a hat-trick and hand City a dramatic 3-2 win over 10-man Bayern Munich at the Etihad Stadium.
The victory was City's first of an otherwise drab campaign and gave them a fighting chance of reaching the knockout stages.
City will now go into their final game in Group E against Roma level on points with the Italian side and CSKA Moscow in a three-way battle for second place.
Kompany told ITV: "If you want to succeed at anything, you need a special player in a special form, otherwise you just don't win anything.
"He's our special player and when he's in that form he makes things achievable that otherwise wouldn't be."
Aguero had put City in control by scoring from the penalty spot after Medhi Benatia had been sent off for bringing him down in the box.
But City looked to have squandered their advantage as Bayern made light of their numerical disadvantage and the absence of a number of stars to reply through Xabi Alonso and Robert Lewandowski.
The game was drifting away from them when Aguero pounced on two errors, in the 85th minute and then in injury time, to turn the game on its head.
The challenge now for City is to build on the result and ensure it becomes a genuine turning point in the club's relationship with the Champions League.
Kompany said: "We are better with our backs against the wall and we now go to Rome, and it will be an incredible game for everyone.
"We have shown with performances in the Premier League that we never give up, and we have done that again.
"If there is one thing we can take out of our league seasons, (it) is that whenever we have won, we have always done it on the back of a number of games that we have had to win.
"It has always looked at some point as if we had lost it, and we have always had to win four or five games in a row
That is when we are at our best.
"That situation is here now, and I am full comfortable that we can go to Rome and get the result."
Aguero, who recently said he wanted to stay at City until they win the Champions League, has now scored 17 in a prolific start to the season.
He said: "I'm very happy for us, the three points are very important
It was difficult but we are happy because this game was very important
It was a game we had to win."
Manager Manuel Pellegrini reiterated his previous belief that Aguero deserves to be rated among the world's elite but wanted to share praise around the team.
He said: "I always said before this night that Sergio is one of the best players of the world, one of the best strikers.
"He played very well but I think also the team played very well, especially in the second half.
"We trusted until the end, we worked, we pressed and finally we could make the chances for Sergio to score."
The equation is still not simple for City, as they will need to ensure they better CSKA Moscow's result against Bayern and still beat or claim a high-scoring draw against Roma.
Pellegrini said: "I am sure that this kind of victory gives a lot of trust to the squad, it is very important, but we will see what happens in the last game.
"I said last week that if we have a mathematical chance to qualify, we will fight to the end
We will see what happens against Roma."
Bayern coach Pep Guardiola felt his side, who had won their four previous games in the competition and are unbeaten in the Bundesliga this season, had gifted victory to City.
The former Barcelona boss said: "I am very, very, very proud of my team
We were playing against the reigning Premier League champions, that is a challenge and we played with 10 men for much of the game.
"But we lost
We gave them the game
Maybe we were tired in the last 10 minutes
We are sad we lost but tomorrow is another day.
"We made two mistakes and that is why we lost
I am sad for the players, they didn't deserve it."
Source : PA
Source: PA