Britt Assombalonga's 97th-minute backheel earned the visitors a share of the spoils at Priestfield.
In-form Assombalonga had earlier slotted home his 14th goal of the season to put Posh in front but they were pegged back after half-time by Joe Martin's free-kick.
"Our effort was fantastic, which I'm very, very pleased with. But a win is never in the bag," Taylor said.
"They're a very good passing team, Darren's building a good team there. We had to hang on in there and it was never comfortable.
"Joe's goal was a great goal, and that was good for us. We knew we had to fight like mad to get back in the game. To be fair I wasn't too unhappy with our first-half performance and we had our chances. I was disappointed with their first goal but we kept on going.
"The late goal hurt, but saying that I think Stuart Nelson also pulled off a couple of brilliant saves. As much as we're disappointed it was such a late equaliser, Peterborough opened us a lot of times and there was some last-ditch defending.
"We've got to get a few more of our decisions right when we're tired."
- Sports & Recreation
- Britt Assombalonga
- Joe Martin