I wouldn't worry about that because basically Newcastle haven't proven themselves better when the opponents are stronger on paper. But if Newcastle can beat Manchester United, Manchester City, Liverpool, Tottenham, Chelsea and Arsenal then I will be worried. But now I wouldn't really worry about them even if the point gap was only 2.
Even so, I think Manchester City also needs to maintain its performance considering the season will be very busy. Manchester City can also be overtaken by other teams including Newcastle and Tottenham. So they have to be really careful about those bad possibilities.
Newcastle have proved that they can compete favorably with other top flight teams in the English Premier league. The played a 3-3 draw against Manchester City, 0-0 draw with Manchester United. They beat Tottenham 2-1 and won Chelsea 1-0. How else do you want them to prove their ability. Newcastle have one of the best teams currently and the management of the club has the financial power to attract and buy more quality players.
I believe Newcastle even have a better chance of performing better than other top four clubs because they are not competing for any continental trophy which means that their players can just focus on winning the premiership.
I think Newcastle should focus more on clinching top 4 position of the league this season, then the next target should be winning the league after beefing up their squad with more quality players in the summer transfer window, if they wanted to focus on winning the league this season they might ended up not finishing on a good position, EPL is a very tough and competitive league, it's better a club set target and meet up with the target for that season rather than chase shadows, I am not undermining the strength and quality of the club, based on past records a newly well funded clubs do perform well after one or two seasons in the league.
The way Newcastle have been performing this season is truly amazing. They are third in the table. And perhaps they have only lost one match this season. Newcastle have no star players. Due to the good bond between the team players, they have been able to maintain the consistency of their performance. But I would say if Newcastle want to qualify for the Champions League they need to strengthen their squad. The team should bring star players. Newcastle's owner is very rich. But we don't know yet whether they are interested in spending money to strengthen the team.