Trailing 2-1, the Seasiders levelled things up at Bloomfield Road in the final minute when Steven Davies raced clear, but Daryl Murphy then nodded home a corner in time added on.
Nouble made it 1-1 after some good work from David McGoldrick after 65 minutes and Taylor put the Tractor Boys 2-1 ahead before the late fireworks ensued.
"It's very disappointing. We pride ourselves on our defence and to lose the game from bad defending is disappointing," Rae said.
"We've scored a lot of goals in the last 10 minutes of games and I thought we'd snatched a point.
"We told them Murphy was a threat from set-pieces - he scored from one against Barnsley last week - but we didn't deal with him at all.
"Given the five players we had out injured it was an incredible effort at Nottingham Forest last week, and here we had to give Bradley Orr an injection just to get through the game.
"We probably lacked that balance with Bradley and Neal Bishop slotting in at the back, and the two weeks we've got now in terms of internationals will be good for us to get bodies back in because we're thin on the ground at the moment.
"But when all is said and done, we've only lost twice in the first three months of the season and we've made a good start."
- Sports & Recreation
- Daryl Murphy
- Stephen Dobbie
- Steven Davies
- David McGoldrick