Both Aguero goals were set up by Gundogan, the first with a quickly-taken free-kick after 56 minutes and the second from an exquisite back-heel soon after the subsequent restart.
Leroy Sane made it three as he combined with David Silva before beating Nick Pope, and Bernardo Silva added the fourth in the last ten minutes after Pope was caught off the line.
"The quality he has inside in the box he has is incredible, I want him to score a lot of goals".
The sliced mishit allowed the ball to roll forward in behind the Manchester City defence where Ashley Barnes finished brilliantly at the near post to give Burnley a shock lead.
"It's an honour for me to have Aguero under my command". They will be without young midfielder Callum O'Dowda who played the full 90 minutes in four of their five EFL Cup matches, but went down with a serious ankle injury in late November.
"The quality he has inside the box is incredible and both of his goals were unbelievable".
"If we want to win something this year, and the next, and the following years, Aguero's presence is fundamental", he said.
"Even in the first half, I didn't have the feeling we weren't playing good, just lacking the opportunity to score a goal".
Guardiola revealed that Silva was due to return to Valencia immediately after the game and continue to "commute" between Spain and England while his son receives treatment.
Yet Lys Mousset reduced the deficit for Bournemouth in the 55th minute and League One leaders Wigan, who won the FA Cup in 2013, were denied a surprise win by Steve Cook's goal two minutes into stoppage-time. The man behind their success, Pep Guardiola, said that he would stay with the club for another year and then see if he deserves to extend the contract.
Despite the early setback, there was no reason to be alarmed for Guardiola and Co. "We've still got some big superpowers to play but I think our mentality is growing, not just the quality of our performances".
"Now he is going back to Spain".
Bristol City have lost two games on the bounce in the Championship and have dropped to fourth as a result. "We can win everything, that's why we are here". "That's how it should be".
"I spoke to the referee and he said I don't have to blow the whistle", Dyche told a news conference.
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