"We scored at the perfect moment. After that it was easier for us to play our game," Modric said. "After the first goal we started creating chances."
"There were also so many fouls in the other box, they could have also given a penalty for us," Rohr said.
Croatia, with Modric and Ivan Rakitic controlling the midfield, dominated most of the match and rarely allowed Nigeria to get close to goal. It took nearly an hour for the Nigerians to have an effort on target -- a header by Odion Ighalo straight at goalkeeper Danijel Subasic.
"We have the youngest team in this World Cup," Rohr said. "Let them learn from this match, from this defeat."
Croatia's victory sent it to the top of the group after Argentina could only manage a 1-1 draw against Iceland.
Modric and Rakitic pushed their team forward and did not allow Nigeria's midfield to reach its fast, young forwards.
The Nigerians struggled to defend Modric's corners, leading to both of Croatia's goals -- the scramble that led to the own-goal and then the foul on Mandzukic that earned Croatia its penalty.
"A win is a win is a win. Corners and penalties are part and parcel of football. What matters is you score," Croatia coach Dalic Zlatko said. "There was some luck there, but we earned our luck."