Aguero scored twice in the 4-1 win.
Burnley, seventh in the Premier League, grabbed a 25th- minute lead when City defender John Stones mis-kicked a Sam Vokes knockdown and Ashley Barnes and the striker burst goalwards before blasting the ball past Claudio Bravo. "I am happy for him to have made his statement and it is not easy for him to travel to Spain and England back and forth".
Guardiola has tended to rotate Aguero with Gabriel Jesus this season to keep both players fresh, but the Brazilian suffered knee ligament damage during City's 0-0 draw at Crystal Palace on December 31 and is likely to be out of action until mid-February. City, who last tasted defeat in domestic competition in their FA Cup semi-final against Arsenal in April, were level in the 56th minute when Aguero fired home from Ilkay Gundogan's pass.
City's own semifinal is just three days away against Championship high-flyers Bristol City, which is quickly followed by a trip to Anfied to face Liverpool in what could be potentially their biggest test left in the Premier League.
"I have to say it's an honour for me to have Sergio under my command", said Pep.
Burnley had been the better side in the first half but City's class eventually told in the second half.
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David Silva, who has been travelling to and from Valencia following the premature birth of his son Mateo, was also back in Manchester for the game.
Burnley have received much praise for the results that they have attained so far this season and it will be intriguing to see whether Sean Dyche's side can continue to perform so effectively in the remainder of the campaign.
While it was an impressive piece of play, the best was to come just two minutes later.
'City have unbelievable quality but they work hard as a team and very well organised. Fatally, the Burnley keeper hestitated, allowing Sane to waltz past him and set up Bernardo Silva for a simple finish.
After that, we had all our confidence back, started to keep the ball and play very well. "We need time to recover perfectly for Kyle and Kevin".
He said: "We think about this every single day and every training session - we can win everything, and that's why we are here".