The north London side were playing out a replay with Sean Dyche's side and found themselves 2-0 down within the opening 10 minutes of the cup clash.
Spurs managed to hit back, however, and ended up prevailing 4-2.
Capoue was one of four different scorers for Tottenham, striking at a crucial time against Burnley - an equaliser just before half-time.
And the midfielder admits his goal was a key moment in his side's comeback victory.
Capoue: "I am very happy despite a bad start we did well to come back. It was important to equalise before half-time." #COYS— Tottenham Hotspur (@SpursOfficial) January 14, 2015
Capoue: "I was in the right place to smash in my goal. It fell to me nicely." Interview on Spurs TV soon. pic.twitter.com/Njel1Z8HD6— Tottenham Hotspur (@SpursOfficial) January 14, 2015
Tottenham were largely unconvincing against Dyche's men, although they did well to secure such a convincing scoreline in spite of that.
One highlight for the north London side was the debut of 17-year-old Josh Onomah after half-time
Boss Mauricio Pochettino, meanwhile, thought Spurs were the better side overall and highlighted Paulinho's opener - just minutes after Burnley went 2-0 up - as another key moment in Tottenham's victory.
Mauricio: "To score so quickly after 2-0 was important for our belief. I think we were the better team overall and deserved to go through."— Tottenham Hotspur (@SpursOfficial) January 14, 2015