[1] He was first called up to a first-team matchday squad for Aston Villa's 2–0 home defeat against Bolton Wanderers in the third round of the League Cup on 20 September 2011, remaining an unused substitute.

[5] He made his senior debut as a 76th-minute substitute for Chris Herd in Villa's 3–0 home win over Tranmere Rovers in the second round of the League Cup on 28 August 2012.

[6] Burke was the joint top scorer in the 2012–13 NextGen Series under-19 club tournament, scoring both of Aston Villa's goals in the final which they won.

[9] He scored his first senior goal in a 4–1 defeat to Oldham Athletic in the Football League Trophy,[10] however Shrewsbury elected to end his loan spell early in October 2013.

[14] On 15 February 2017, Burke signed for his hometown club Shamrock Rovers, being described by manager Stephen Bradley as an "exciting talent".

[23] He scored a penalty against ŠK Slovan Bratislava in UEFA Champions League first qualifying round, but Rovers were eliminated 3-2 on aggregate.

In doing so, he became the first home-based Irish international goalscorer since April 1978 when Ray Treacy, also of Shamrock Rovers, scored for the Republic of Ireland against Turkey.