Cywka appeared in Derby's opening fixture for the 2010–11 season, an away match against Leeds United, in which the Rams won 2–1. His first goal for the club came on Saturday 14 August 2010 in a match which finished 2–1 to the visiting Cardiff City. Cywka suffered a fractured cheekbone in the same match. He quickly returned to action, however, and grabbed this 2nd and 3rd senior goals with a brace in a 4–1 win over Watford on 30 October 2010, which earned him a place in the Championship Team of the Week. Cywka again started against Portsmouth at Pride Park and won a penalty after being fouled in the box, Robbie Savage scored the opener from the spot and the Rams went on to record a 2–0 victory. His 4th goal came in the 3–2 victory over Scunthorpe United, scoring within the first 5 minutes.