Cywka found himself out of the side for the start of the 2011–12 season as Derby made their best start to a season for over 100 years. His first league appearance came in the seventh fixture, away at Nottingham Forest, but he was withdrawn after just four minutes when the dismissal of Frank Fielding led to the need for a tactical reshuffle. Three late substitute appearances followed before he earned his second start of the campaign in the twelfth match of the season, away to Reading, when injuries had left Derby with just Cywka and Theo Robinson to choose from amongst the club's strikers. In the event, Cywka scored his first goal of the season in the 75th minute to give Derby a 2–1 lead in a match they eventually drew 2–2. After a succession of poor performances and losing his place in the first team, Cywka was told by Derby manager Nigel Clough in January 2012 that he was free to leave the club on a free transfer. This followed the news that a move to a Polish club had broken down, which later turned out to be Ekstraklasa leaders Śląsk Wrocław.