The Millers, who won their final five games of last season to win promotion, have made a flying start to life in League One, sitting in fourth position following an unbeaten opening six games.
Boss Steve Evans has built a strong squad, with several options in each position, and Skarz - a summer signing from Bury - reckons that players know they have to be at their best to stay in the team.
"I am pleased with how I have started the season," he told Press Association Sport.
"I always want to do better and improve myself as do all the lads here.
"There are a lot of quality players here who work really hard in training to try and improve themselves day-by-day and I am no different.
"That is one of the reasons why competition for places is so high because all the lads want to improve themselves and that's why we have done so well.
"I have been pleased with how I have started, but want to improve."