The defensive duo are currently on international duty, and Dummett's Wales face Clark's Republic of Ireland at the Cardiff City Stadium on Thursday evening.
Both players started in the Magpies' narrow defeat to the reigning Premier League champions last weekend, and although Rafa Benítez's side only have one point to show from their opening four league games, Dummett felt there was plenty at the Etihad Stadium for United to build on.
"We took them all the way to the end of the game - they even brought on (Vincent) Kompany to try and hold onto the lead they had," the ever-reliable left-back told nufc.co.uk.
"We had a game plan and it nearly worked again. At the end of the day, we've got no points again but the team spirit was there all through the game, so we can take the positives and try to progress in the games in the future.
"We've played against some really tough teams, a few of the best teams in the league, so it's been a tough start for us. But we've got a real good team spirit and a desire to work hard together and try to produce the results we got last season, to try and finish in a good position again.
"I think you can see in the performance that everyone was fighting for each other. Stuff in the press, we try not to read into too much; things happen in training, people want to win, and things got made out to be worse than they were but I think you can see from the performance that we were all working hard together."
On Thursday, however, Dummett and Clark will be rivals for 90 minutes as Wales and the Republic of Ireland take their first steps on the road to Euro 2020.
"It'll be nice if I can get some minutes in that game and hopefully he does as well - but we beat them," said Dummett.
"We know it's going to be a tough game for Wales but hopefully if I play, I can get a good performance for my country and try to win the game."
Dummett took a break from international football in 2017 in order to focus on his club career. At the time, he had played through the pain barrier on several occasions to help Newcastle return to the Premier League, but he had always made it clear that he hoped to represent the Dragons again in the future.
Former Manchester United legend Ryan Giggs replaced Chris Coleman in January, and named Dummett in his first competitive squad for Wales' inaugural UEFA Nations League matches.
"When I spoke with the manager, he said the door was always open and he's made numerous phone calls, and I spoke with the assistant manager and they made it clear that they wanted me back in the squad," explained Dummett, who has two caps for Wales having previously represented them at youth and under-21 level.
"It was the right thing to do for me and I've been fit for a long time now, and I just want to try and get involved with the team and try to get some minutes for Wales."
