The 22-year-old, who is principally an attacking midfielder, was initially seen as a temporary solution in the position after injuries to Benjamin Mendy and Fabian Delph but he is now holding his own.
Guardiola's faith in him has been underlined by his selection for the last three crucial Premier League games against Tottenham, Manchester United and the Clarets despite Mendy's return to fitness.
City needed to win all three - and did - to return to the top of the table above Liverpool and remain in control of the title race.
"It will only be a fantastic season for me if we win the title," said Zinchenko, who has remarkably won all 20 Premier League games in which he has played since December 2017.
"In this case everyone has to take responsibility, and everyone is ready to do that.
"You can see how tough it was (on Sunday) but the important thing is that we have three massive points."
City overcame another tough obstacle at Turf Moor, finally wearing down a spirited Burnley side to prevail courtesy of a scrambled Sergio Aguero strike that only crossed the line by millimetres in the 63rd minute.
The goal rewarded City for a sustained spell of pressure early in the second half and they created numerous other chances but it still remained a tense affair. Burnley frequently disrupted the champions' usual rhythm and the final whistle was eventually greeted with huge relief.
Zinchenko felt it was a hard-earned victory.
He said: "We should have started like we did in the second half from the beginning.
"The manager said that at half-time, and that we had to play quicker. It didn't matter that the pitch was dry and other things.
"We had to try to play quicker, not take that extra touch, and just show our desire to win the game. You can see that we did it."
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