The German, who won the season-opener in Australia, started from pole at the Sakhir circuit 11 days ago but lost his lead off the line, with Hamilton moving from second to head the field into the first corner.
The 28-year-old Rosberg was unable to find a way past his team mate in a wheel-to-wheel duel, with only one second separating the Mercedes pair at the finish.
Rosberg said there was one incident where he felt the 2008 world champion pushed things too far in defending his lead.
They spoke about it after the race but he anticipated having a further conversation with Hamilton and the team before racing begins in Shanghai.
“It’s completely normal that as a team when there is situations or races where a lot has happened and which are intense battles that you are going to sit down and discuss,” Rosberg told reporters on Thursday.
“The only example which I thought was above the limits was where I came on the radio. All the other examples were really tough racing but with the necessary respect, so that’s it.”
The two drivers drew plenty of plaudits for the way they contested the race, as did Mercedes for not issuing team orders.
Heading into this weekend’s race, Rosberg leads the standings on 61 points. Hamilton, who retired in Australia, trails by 11 points after winning the last two races.
Rosberg, son of 1982 world champion Keke, is keen to get his own back at the scene of his maiden race triumph in 2012 and is determined to prevent Hamilton winning three consecutive races for the first time.
“I know I can win here, that I have the chance to win here, and I know most likely it’s going to be against Lewis, so that’s where my mind is at the moment.”