Republic of Ireland international Treacy came off the bench to rescue a point by scoring with almost his first touch after Tokelo Rantie had headed Bournemouth in front.
Relieved Dyche, whose side remain unbeaten in the Sky Bet Championship since Boxing Day, said: "We were well below par.
"But we have built an amazing mentality here so that when five or six players are not at their best we can still come away with a point.
"There was no sign of us wilting or going under after they scored and we limited them to few chances.
"It was nice for Keith to get a goal. It was a great run and a great finish.
"We want the players out of the side to be ready to come on and affect the game and they certainly did that."
The match only went ahead after an early-morning pitch inspection by referee Graham Scott and Dyche admitted his side struggled to adapt to the damp and windy conditions on the south coast.
Dyche added: "Bournemouth played the conditions better so I will take a point because that is seven points in a week which is another big statement to what we are trying to achieve here."
Record signing Rantie gave Bournemouth the lead six minutes after half-time, rising unchallenged to head Ian Harte's corner past the helpless Tom Heaton and claim his third goal of the season.
Clarets boss Sean Dyche responded to falling behind by making a double change, bringing on Treacy and Ross Wallace in place of the ineffective Michael Kightly and Scott Arfield.
The move paid immediate dividends when Wallace broke down the right and his cross-cum-shot deflected kindly into the path of Treacy who lashed the ball into the roof of the net at the far post.
Bournemouth were denied a late winner by saves from Heaton to deny Lewis Grabban and Tommy Elphick while Cherries defender Simon Francis also struck the bar four minutes from time.
Home boss Eddie Howe backed Rantie to hit the goal trail after helping the manager take a point from his former club.
Howe said: "All strikers need goals and Tokelo is no different. He is improving all the time and getting more confident - he has a bright future.
"We worked on that corner routine before the game so it was good to see it come off.
"It was a great delivery from Harte and good movement from Tokelo to get on the end of it. It is something we work on all the time and we had a refresher before the match."