Krstičić began his career at OFK Beograd and joined Sampdoria on 1 September 2008 at the insisting of Giuseppe Marotta, who believed the 17-year-old was one of the most talented players he had ever brought to the club. While playing for the youth team, he played in the 2011 Torneo di Viareggio as one of the allowed over-age players. He suffered a knee injury and had surgery performed to correct his meniscus injury, after which doctors unexpectedly diagnosed him with Burkitt's lymphoma and allegedly told Krstičić he had 48 hours to live. Luckily, Sampdoria's medical staff was able to reverse the cancer growth and Krstičić lived on to play football, although the condition was a great setback in his career. Over the course of his cancer episode, Krstičić lost 55 pounds and his blood was compromised. Krstičić finally made his debut for Sampdoria in a UEFA Europa League match against Debrecen on 16 December 2010. On 2 December 2012, he scored his first goal for Sampdoria against Fiorentina. On 2 February 2015, Krstičić was signed by Bologna in a temporary deal. The club also signed Júnior Costa and Daniele Gastaldello from the Genoese club outright. However, Krstičić was injured in March. His contract with Sampdoria was terminated on 18 July 2016.
On 25 July 2016, Krstičić signed for La Liga side Alavés on a free transfer. Fellow countryman Aleksandar Katai, who also suffered from a serious illness earlier in his career, joined Alavés later the same summer, and the two became midfield teammates.
On 26 December 2018, Red Star Belgrade announced that Krstičić's transfer to AEK Athens had gone through. The Athens based club activated his release clause of €500,000, six months before the end of his contract with Red Star, which saw him move to his new club. On 23 January 2019, he scored his first goal for his new club in an emphatic 5–0 home win against AO Chania Kissamikos for the Greek Cup round of 16. His team won 6–1 on aggregate and advanced to the quarter finals of the competition. On 3 April 2019, by lashing the ball across from the right wing, Viktor Klonaridis picked out the onrushing Krstičić, who prodded it past the beaten Nikos Melissas in a 2–0 Greek Cup semifinal 1st leg against Lamia. On 2 February 2020, AEK Athens escaped from Peristeri with all three points thanks to Nenad Krstičić header, whose solitary goal gave Massimo Carrera’s side a narrow 1–0 win over Atromitos. It was his first goal for the 2019–20 Superleague. On 19 February 2020, he scored with a close tap-in in a 4–0 home win against Panetolikos for the Greek Cup quarter finals.
