Aguero rose to angle a superb effort into the bottom corner from 10 metres to give City a 3-1 win over Everton and 4-3 aggregate success in their semi-final clash.
It was Aguero's fifth goal in his last three matches, after doubles against Crystal Palace and West Ham United, and showed his manager that he had completely recovered from the injuries that blighted his early season.
Aguero, who has now scored seven goals in his last seven games, endured a stop-start beginning to the campaign and was sidelined for seven games with a hamstring injury picked up on international duty.
Having scored 26 league goals last season, he netted in only three of his first 12 Premier League outings in 2015, with Pellegrini facing weeks of questions about when the striker would return to form.
"Tonight he scored the best goal, had a shot that hit the post and he is always making a lot of danger, so I think he is back to his best," Pellegrini told Sky Sports.
City, who will be playing in their fourth major final in the last six seasons when they face Liverpool at Wembley on Feb. 28, were off the pace for much of the match.
They fell behind after 18 minutes to Ross Barkley's superb individual goal and were perhaps lucky to claw their way back into the match when Fernandinho's shot was deflected into the net to make it 1-1 on the night.
Their good fortune carried on into the second half when Kevin de Bruyne put the hosts ahead, but only after Raheem Sterling had failed to keep the ball in play before cutting it back for the Belgian to sidefoot home.
The decision to let the goal stand incensed Everton manager Roberto Martinez, who was hoping to steer his side to their first cup final in seven years.
"Everyone that has seen the replay can clearly see the ball is out of play," he told the BBC.
"City are a very good side. If they score three goals in the right way then you accept it. The first goal was a deflected shot, but the second goal the ball was clearly out before it was crossed in."
(Reporting by Toby Davis; editing by Ed Osmond)
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