Raheem Sterling's first half finish gave the Premier League champions a brief lead before Jetro Willems' first goal at St. James' Park put the Magpies on level terms.
Newcastle held firm against Pep Guardiola's side but were dealt a difficult blow in the latter stages as Kevin de Bruyne's wonder strike regained City's advantage but, once again, United equalised in quick fashion as Jonjo Shelvey's brilliant strike in front of the Gallowgate End secured an impressive point.
"It was a tough game," Dúbravka told nufc.co.uk. "We were all working really hard and I think we did everything that we could do to take one point. I'm happy with the guys' performance because everybody did what they trained and prepared for. It was a great team effort.
"It was a great reaction (after the Villa game). It was not our best night to play against them but today was a bit different and we played also a different way to be successful.
"I'm quite happy because when you're playing against Man City, you can expect to be under a lot of pressure and they certainly pushed us but the reaction from the players was amazing.
"We were pleased with the way we responded after conceding both goals, especially with Jonjo's goal when it came in the final minutes of the game. It was an amazing strike!
"It is about emotion when you score and I enjoyed myself in celebrating that goal. From my point of view, it looked like he had struck the ball into the top corner so I was very happy, especially after conceding earlier."
Following the draw, United now head into December on 16 points and face a busy winter schedule, with the Magpies set to play six league fixtures in the final month of 2019.
However, Dúbravka is hopeful his side can continue their impressive home run, with United undefeated at home since their opening day against Arsenal and the Slovakian believes the draw against Man City can strongly benefit the squad ahead of a hectic Christmas period.
"Hopefully we can continue the good form at home," the 30-year-old added. "It isn't easy to break us down, especially at St. James' Park, and hopefully we can play a similar style of the game away from home so we can collect more points. Every point is important for us at the moment, especially against the top sides.
"We need to keep the momentum from this game. The confidence should be high and every time when you take the points from the top sides, you need to have that confidence.
"Hopefully, we can take this great feeling and mood after the City game into the next one (against Sheffield United) and create more chances because we'd like to win games as well."
