The Russian world number eight said he was "almost dead every day" and could barely sleep this week after securing a career second Masters 1000 victory.
Rublev had lost four consecutive matches before arriving in the Spanish capital but came from a set down to beat his Canadian opponent.
The 26-year-old triumphed at the Hong Kong Open in January but struggled since before turning around his form in Madrid, dropping just one set on the way to what proved a tense final.
"I think it was an incredible match, Felix deserved (in) the same way as me to win today and we showed a great battle together, I think the most important thing was that the people enjoyed it," said Rublev on court.
"Our sport is like this, we cannot have both winners."
Rublev, who takes the Madrid crown from double champion Carlos Alcaraz whom he beat in the quarter-finals, said he had played despite feeling ill at times this week and hailed his doctors for helping him through.
"If you knew what I had been through in the past nine days you would not imagine that I would be able to win a title," he added.
"I was almost dead every day, I was not sleeping at night -- the last three, four days I didn't sleep."
Auger-Aliassime reached the final after his opponent Jiri Lehecka retired hurt in the semi-finals and quarter-final opponent Jannik Sinner withdrew with a hip injury, with the ATP draw at the clay-court tournament struck by misfortune.
However the 23-year-old Canadian, ranked 35th in the world, gave everything he had in his first Masters 1000 final appearance.
Tense battle
Auger-Aliassime started superbly by breaking to love in the first game and then again in the fifth game for a 4-1 lead.
Rublev recovered a break when Auger-Aliassime went long, and consolidated for a 4-3 deficit.
The Russian saved a set point to hold for 5-4 down but Auger-Aliassime clinched it at the second opportunity with a forehand down the line.
In the second set the Canadian held for 3-3 with a brilliant drop shot after Rublev spurned a break point.
They stayed on serve until the 12th game when Rublev brought up two set points, converting the second to take it to a deciding third set.
Rublev raced through his service games and put heavy pressure on his opponent's serve, forcing a break point in the second game and two more in the fourth, none of which he could take.
Auger-Aliassime produced huge serves to fight his way out of tough spots, racking up 14 aces in the match to Rublev's seven.
However Rublev dropped just three points on his serve in the third set, while Auger-Aliassime trailed in all of his service games but always battled back, until the decisive 12th game.
Auger-Aliassime double-faulted to hand Rublev the title, with the Russian falling to the floor in delight.
