The reigning world champion, who won the first race of the season in Bahrain, started P15 on the grid after a drive shaft failure scuppered his qualifying on Saturday.
Despite another Red Bull one-two Verstappen was unhappy in the post-race press conference, emphasising that he is “not here to finish second.”
Rosberg, the 2016 world champion with Mercedes, was decidedly unimpressed by Verstappen’s reaction in light of the team’s success in Jeddah.
“It is not good to see,” Rosberg told Sky F1. “We were also told he skipped the team meeting [on Saturday] apparently.
“I don’t think it’s a good approach of mentality so early in the season when the team has done such a brilliant job and worked so hard. I think he could be more gracious.”
In full, Verstappen said: "It’s not only about the pace of the car, we need to make sure we are reliable without any issues,” he told reporters after the race in Jeddah.
“My first weekend was not very clean because of just the big balance shift from testing to the race weekend, some other things which were going on in the background.
"Now again, after three positive practice sessions, I have an issue in qualifying. Of course, I recovered to second which is good. In general the whole feeling in the team, everyone is happy – but personally I’m not happy because I’m not here to be second.
"Especially when you are working very hard back at the factory, to make sure you arrive here in a good state, and making sure everything is spot on. Then you have to do the recovery race.
"I don’t mind doing it, but when you are fighting for a championship, when it looks like it’s just between two cars, you have to make sure those two cars are reliable.
“We have to do better, absolutely. Just to have a cleaner weekend, I think that would be nice."
The Dutchman does lead the World Championship however after securing a bonus point for setting the fastest lap of the race on his final lap.
Verstappen will next be in action at Albert Park in Melbourne for the Australian Grand Prix (31 March-2 April) – a race he is yet to win and retired from last year.