They both seemed satisfied following an even first leg that ended in a 1-1 draw and left the Champions League semi-final wide open going into next week's return match in Manchester.
Vinicius and Kevin de Bruyne scored with long-range strikes in a match in which Madrid's defence successfully kept Haaland — the Champions League's leading scorer — from being decisive.
"I think both teams have the feeling that it was a good result," said Madrid boss Carlo Ancelotti, who took charge of his 190th Champions League match.
"Maybe we played a bit better to deserve a victory, but it's a series that will be even until the last minute."
Madrid beat City in last year's semis and went on to win a record-extending 14th Champions League title, while the English club again fell short of European success.
"It was an even match," City manager Pep Guardiola said.
"They scored when we were better and we equalised when they were better ... Manchester will be like a final in front of our own fans."
The first leg of the other semi-final between Italian rivals Inter Milan and AC Milan is on Wednesday.
City controlled possession but couldn't translate it into significant scoring opportunities. Erling Haaland wasted a few chances early on Tuesday night but wasn't much of a threat throughout the game.
The Norwegian came into the match having scored 12 of City's 26 goals in the Champions League this season and was five short of Cristiano Ronaldo's single-season record of 17 for Madrid in 2013-14.
Vinicius opened the scoring in the 36th minute with his seventh Champions League goal this season. The Brazil forward picked up a pass by Eduardo Camavinga and used one touch to set up his right-footed shot from outside the area.
City struggled to get close to Madrid's goal but De Bruyne found the net in the 67th with a firm one-timer from outside the area after the home side lost possession because of a poor pass across the field by Camavinga.
"It was a shame that we conceded that goal," Madrid midfielder Luka Modric said.
"I think we deserved more. They had more possession but didn't create a lot of chances. It's still 50-50 and we will go into the second match with confidence."
Haaland had not yet joined City when they lost 6-5 on aggregate to Madrid in last year's last four tie.
Madrid are making their 11th semi-final appearance in 13 seasons and trying to win a sixth title in 10 years. City played in their first Champions League final two seasons ago, losing to Chelsea.
Madrid won the Copa del Rey title last weekend but are virtually out of contention in La Liga and can fully focus on City. The English champions remain in a tight Premier League title race with Arsenal.
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