[3] On 26 February 2015, he made his UEFA Europa League debut as a substitute replacing Rodrigo Palacio in the 89th minute of a 1–0 home win over Celtic.

[4] On 4 April 2014, Pușcaș played his first match as a starter for Internazionale, a 1–1 home draw against Parma, he was replaced by Mateo Kovačić in the 46th minute.

[6] On 9 August he made his debut for Bari as a substitute replacing Anthony Partipilo in the 60th minute of a 2–1 home defeat against Foggia in the second round of Coppa Italia.

On 7 August he made his debut in a match loss 4–2 at penalties after a 0–0 home draw against Salernitana in the second round of Coppa Italia; he was replaced by Fabio Mazzeo in the 68th minute.

[15] Pușcaș started his second season with Benevento by playing 80 minutes in a 4–0 home defeat against Perugia in the third round of Coppa Italia.

[17] On 3 December 2017, Pușcaș scored his first Serie A goal in the 2–2 home draw versus Milan that gave Benevento their first ever point in the top flight.

[32] Pușcaș scored his first EFL Championship hat-trick against Wigan Athletic on 30 November 2019 in a 3–1 victory, with the goals all coming in the space of 4 minutes 54 seconds.

In 2013, the then-Hungarian head coach Sándor Egervári went to watch him play in the Romanian second division, but gave up on him[39] by saying that there are already players of his ability in Hungary.

[40] Pușcaș scored seven times for Romania under-21 in the 2019 UEFA European Championship qualifiers, as his side won its group and progressed to the final tournament in Italy.