The left-back, a summer signing from Bury, has played an integral role as the Millers have built on last term's promotion by remaining unbeaten in their opening seven games in Sky Bet League One.
Saturday's come-from-behind win against Oldham leaves Steve Evans' men in fourth position, but Skarz is not getting carried away.
"We have had a really good start but we know in football we can't get ahead of ourselves, so we are just enjoying playing the teams that we are playing," he told Press Association Sport.
"But we know we can't get complacent, every team in this league is difficult with everyone posing different threats.
"League Two was a good league last season, but in League One if you make a mistake you get punished and nine times out of 10 it ends up in the back of the net.
"The added bonus for us is the teams we are playing, the likes of Sheffield United and Bradford, there are some nice stadiums and it is something all the players are relishing."