The Clarets controlled much of the possession at Turf Moor without really threatening Boro's goal on Tuesday night.
Middlesbrough have got big-name players in their squad and Dyche is taking comfort from the fact that Tony Mowbray's side opted for a defensive approach in Lancashire.
"We played well for a large part of the game, kept the ball and dominated the possession stats and chance stats without really opening up that one clinical moment to finish it," said Dyche.
"It's a knife-edge sort of feeling. That's a side who are sixth and have got a lot of big players and they've come here and defended. That was the intent.
"It kind of shows how far we've come as a team and as a club to be recognised as someone who is still in there with a real chance of chasing the dream."
That dream of a play-off place lies seven points beyond the Clarets at present and Dyche hopes the unpredictable nature of the Championship can work in their favour.
"We all know it was important not to lose," he added. "It was quite clear the way we played we didn't go with that intent, we went to win.
"But it keeps us in that pack who are hunting, among the others. It's a crazy division, as we all know, so we're looking to do that crazy thing - win lots of games."