City's double goalscorer Gundogan said: "The result was maybe ideal but the way we played there are still plenty of things to improve".
Throw in a 16-point lead in the Premier League and this coruscating form, and a belief that all things are possible might start to course strongly through City and all its supporters.
"We will go into the League Cup final [against Arsenal] with the same kind of preparation and self-belief as we did for the game today and as long as that doesn't change, and the intensity stays at that level, every game is going to be exciting". OK, we could be more clinical but it was 4-0.
A brilliant Vaclik save denied Gundogan a hat-trick late on but, even so, the second leg looks little more than a formality for Guardiola's side. "Ilkay is a guy with special quality, he is an fantastic midfield player who has a sense for goal", Guardiola said.
"When I see him play I realise how we missed him last season".
"With De Bruyne and David Silva, we have a fantastic midfield trio".
"We have shown that we were the better team tonight and only for a lack of motivation and effort could we be not that team again at the Etihad and that's not permitted".
Kompany's appearances has been limited due to injury this season and has only featured in 10 Premier League contests, last having played against Burnley on 3 February.
Guardiola said the return of Silva and Leroy Sane, who both came on in the second half, boosts City's chances in the coming weeks.
"He's a guy with special qualities", said Guardiola. Like we said in the beginning, game by game.
Sane's return from an ankle injury after only two weeks was a surprise with the German back - a month ahead of schedule.
Basel coach Raphael Wicky admitted his side were outplayed by a ruthless City side.