Until his 97th minute effort Josh Maja's second-half penalty had looked likely to give the Cottagers a hugely valuable three points in their battle against relegation.
Parker later said, "I'm disappointed and gutted and the overriding factor is the team have worked tirelessly today, given everything, come to a place like this against a very good side and manged to get our nose in front. Second half we had to weather it a bit and then the last action, I've just seen it back. He [Rob Holding] looks offside to me, he's standing in an offside position. As a consequence of where my keeper is, he's two yards away from the goal line and he's in an offside position - that's what's disappointing.
"We defended superbly, we limited them to few chances the longer the game was going on I felt we had done well but the residing factor is that late decision and the rules on it. I think the linesman sees Holding in an offside position we then go to someone who is miles away and I'm not just saying that because I'm standing on the end of a draw if someone's standing in an offside position then I don't understand that."
On the result feeling like a loss, he continued: "It does when it comes that close, we wanted to win the game, we needed to win today, we need to win next week and the remaining games. We were so close today so it's been painful. As disappointed as I am now and the team are we'll wake up tomorrow and we will fight again and keep going. You see a team with effort, desire, with spirit and with that we've got a fighting chance."
On looking at other teams' results, Parker concluded: "The main focus is our game of course, when you get to this point in the season you always have an eye on other results but the most important thing is us winning games in this division and if we can't we won't stay in it. We've not managed to win today, I feel unfairly.
"I'm immensely proud of the team and the journey they have been on and I often say a young team lacking Premier League experience and the journey has been an incredible one - they've given me everything and people will point fingers and say where we've failed and rightly so but there's one area we have never failed and that's desire and spirit and that's the reason we still have a fighting chance. I'm proud but passion and spirit don't win games, we need to win games, we will try to do that."