The Spain right-back feels Pep Guardiola’s side did not prove themselves “superior” at the Bernabeu.
Dani Carvajal insists Real Madrid have nothing to fear heading to the Etihad Stadium for the second leg of their Champions League semi-final next week.
The tie is delicately poised at 1-1 after a pulsating draw in the first meeting between the sides at the Bernabeu on Tuesday.
Vinicius Junior fired holders Real into the lead with a stunning strike in the first half but Kevin De Bruyne levelled with an equally brilliant effort in the second period.
Real right-back Carvajal said: “They have world-class players, they move the ball very well, they’re tactically very well worked – but I don’t think we saw a City side that are superior to Madrid.
“The team goes home knowing that we played well and that if we get things right, if we take our chances in Manchester, we have a chance of going through.
“We go there with nothing to fear. We have to go there to win, to play our game, and the team believes in it.”
City dominated early on at the Bernabeu but it was Real that took the lead against the run of play when Vinicius lashed home from 25 yards on 36 minutes.
From then on the hosts did their best to disrupt City’s flow by employing some rough tactics.
Carvajal particularly pushed things to the limit and was involved in a running battle with Jack Grealish. At one point he barged the England midfielder into the advertising hoardings and then fell to the ground theatrically when Grealish reacted angrily.
“It’s a semi-final, everyone is playing to the limit, every challenge is a war,” the Spain international said.
City drew level on 67 minutes, during a period when Real had been dominating, when De Bruyne connected with a fierce drive from a similar range to Vinicius.
The draw was the least the Premier League leaders deserved but Real did have a gripe over the equaliser, with suggestions the ball may have gone out of play in the build-up.
Real manager Carlo Ancelotti was booked for his protestations as De Bruyne celebrated.
Carvajal said: “In general I think the referee (Portugal’s Artur Dias) was good, he controlled it pretty well. It’s complicated to referee a Champions League semi-final.
“We have to congratulate him for that but if the ball did go out then that’s an error that could cost us the tie.”