Burnley were staring down the barrel of defeat as they trailed 2-1 at half-time, with goals from Steven Taylor and Jack Colback either side of Paul Dummett's own goal handing Newcastle the deserved advantage at St James' Park.
However, the visitors were much improved after the break as first Danny Ings levelled proceeding, before George Boyd's 86th-minute effort cancelled out what looked like the winning goal from Moussa Sissoko.
Burnley hit the woodwork four times in an impressive display that left manager Dyche with plenty of cause for optimism.
"The belief was still there and I thought some of the quality of our play was exceptional," he said.
"Going into Christmas people said we might not win a game, but we have taken five points from five teams in the top 10 and two in the top four.
"We still need to get more points, but we are going in the right direction and the performance levels are very high."
Dyche was hindered by three enforced substitutions in the first half, with Jason Shackell, Dean Marney and Kevin Long all going off injured - the latter taken from the pitch on a stretcher with a serious-looking knee injury.
"We had to make three changes and it was all going off in that first half," Dyche added.
"We had to deal with it and after that I thought we were outstanding, right to the death when we were still looking to score."
Burnley remain in the relegation zone, but are just one point from safety after 20 matches.
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