Since 2017, 's main rival, with the Italian ending up as runner-up in the championship for two years in a row.
He is again second in the standings nine races into the 2019 season, with teammate lies only six points further back in third.
But while both Ducatis have struggled in recent rounds, Yamaha has found strong form with scoring two pole positions.
Marquez said that the Barcelona race, where in one crash and handed his teammate an easy win, changed the championship.
"Until Montmelo it was one championship, now from Montmelo to here it’s another championship," he said. "We have two [wins worth of points] between me and Dovi.
"Of course, Ducati will come back and they will be very fast, but at the moment the riders to beat are both Yamahas, Vinales and Quartararo, I think they will be the fastest in the second part of the championship."
Petrucci agreed that Vinales is now a "problem" in terms of the championship.
"I am happy about my situation in the championship because I am P3 and I gain some point from Rins that is fourth, but he crashed," said the Ducati rider.
"Now the problem is Maverick that is gaining some points but for fight with these guys we need something more.
"I want to work more not because I need, but because this makes me more hungry for the rest of the season, give me more motivation because I want to finish in the top three position.
"It is very hard at the moment but I think we have to believe and especially at home they have to work and believe that still everything is possible."
The second part of the season will begin with Brno and the Red Bull Ring, two tracks where Petrucci believes Ducati should perform better.
However, he pointed out that Marquez was only beaten by a very small margin at both Qatar and Mugello, two tracks where Ducati has historically held an edge over Honda.
"For sure these two tracks are a little bit better compared to the past two we had," Petrucci added.
"Marc this year made a bigger step compared to us, we fought hard with him in Qatar and Mugello where always been two Ducati tracks and the next two are the same, two Ducati tracks.
"But in Qatar and Mugello we won by thousandths. We need to give all for trying to keep the championship open."