Spurs' boss Mauricio Pochettino had seen his side win at Swansea last Sunday and then beat Newcastle 4-0 in the Capital One Cup in midweek before this win saw them move into sixth place in the Premier League.
"It's been a great six days, three games, three victories," he said. "It's been a very important week for us and I'm happy for the players and for our supporters.
"Burnley scored with their first shot and that's always difficult, They were a physical team, playing balls up to a strong striker but we're fighting and we played well.
"It wasn't easy for us after three games in a week and it was important to show character. We never give up, we keep fighting and keep going. I think we played very well for long periods.
"I think in the end the result didn't reflect the performance because we deserved more of a gap in the scoreline, but in the end, three points is very important to us."
Three points is what Sean Dyche and the Clarets didn't get, but he saw enough from his team to know we are heading in the right direction.
"I'm proud of that today," he said. "We wanted to play an effective game and we wanted to get the ball forward quicker than we have been doing. We felt we could affect the game with that and we did.
"I think Ashley Barnes and Danny Ings were sharp. We made chances and we were solid in our shape but one of the goals is a poor goal for us to concede. The other goal? I'm a bit disappointed with the decision, I've got to be honest, because Keano is behind it. It takes a flick off Harry Kane and it's ball to hand for me because Michael can't do anything about that.
"Then they play a quick free kick and we all know the debate of offside. Their lads steps out of the way and that's got to be interfering, but it wasn't deemed so and they run through and score. The reason I say it's interfering is because if that's in the lines of the box then surely it is.
"I was disappointed in that moment because it cost us dearly, but other than that there were a lot of good signs today.
"I speak about the growth of the players a lot because they are improving and getting more experienced to come to this stadium and perform in that manner. That's a fine show of where we are going and where we are heading.
"We come away disappointed in the result but not the performance. There is certain a future in the performance."
Our goal was a second in successive games for Ashley Barnes and Dyche added: "Ash is on an upward curve at the minute, not just with his goals but his general performances. I only took him off towards the end because he ran out of legs a bit after getting absolutely everything.
"Our fans were terrific again today and they know we want to play on the front foot when we come to these places and we've earned the right. We will be aggressive in our play, we're not looking to contain.
"A good marker for all to see today is that we went to the Emirates and came off the front a bit. It didn't work out so I said to the players, we go braver, we get our distances and we did that.
"It's not an easy place to come and play as they've got some highly technical players that were brought in for multi millions and they've turned a corner recently with their results, but we'll debrief this and then go again because I think the fans believe and we certainly believe there is more to come."