Rose's goal left Dyche fuming that the man responsible for the through-ball, Spurs midfielder Moussa Sissoko, had not been sent off moments earlier for a high challenge.
The 2-1 win ensures Spurs remain in contention for a top-four finish in the Premier League, particularly after Arsenal's loss at Manchester City - just one point now separates Spurs from Arsenal and Liverpool, who both have 34 points.
"The boss always says that he wants me to play with the same arrogance as Marcelo at Real Madrid". I think our position is good, now we are winning games and we are a little bit closer to the second position.
Dele Alli equalised but a combination of poor finishing, organised defending and Burnley goalkeeper Tom Heaton kept the hosts at bay until Danny Rose s 71st minute victor.
"He stays on and immediately sets up the victor, so obviously I am very frustrated on that score because we played some good stuff today and deserved something from the game".
Sissoko, on for Dembele, was lucky only to receive a yellow card for a high tackle on Ward and Burnley's sense of injustice was compounded when the Frenchman laid on Rose's victor 20 minutes from time.
Instead it was Burnley - who last beat Spurs here in 1983 but looked risky on the counterattack and battled for every ball - who took the lead through Ashley Barnes after 20 minutes.
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Kane is clearly Tottenham's most clinical finisher - he's scored an impressive seven goals with those 35 shots this term.
"We are a work in progress, but we have taken strides forward in the last couple of games", Dyche said.
However, six minutes later Dele Alli atoned for his bad second-minute miss by running into the Burnley box and tapping in Kyle Walker's low cross. "Mauricio Pochettino has done a brilliant job there along with his players, and they're a force to be reckoned with this season without a shadow of a doubt. For us, it is our first step", Pochettino told Sky Sports. The first choice full back for club and country, Rose is one of the best players in his position in the league and also in Europe. I asked him, the ref.
"We're thankful now for the ten-day gap between matches, but it would be nice to keep our run going".
"There were more things that maybe made it hard for us to compete at our best and I think now we are in a good position to try to achieve good results".
It's still a long way to the end of the season.
Tottenham, who trail Chelsea by 10 points, beat Burnley 2-1 at home on Sunday to stay fifth in the table, a point behind north London rivals Arsenal.