With Shots sitting 21st and the Pilgrims 22nd at the start of play this was a relegation six-pointer in every sense of the word, and first-half goals from Jason Banton, on loan from Crystal Palace, moved Argyle two points clear of the drop zone while sending the Shots into the bottom two.
A Peter Vincenti strike for the hosts was sandwiched either side of Banton's goals but it was not enough.
Holdsworth said: "On another day we would have taken something from the game.
"We've hit a post, we had numerous chances, at 1-1 I thought we were going to go on to win the game. We're all disappointed but there are 16 massive games to go.
"If I was standing here and we'd won the game that might be a bit harsh on Plymouth. They did some good things and counter-attacked us well. I think we deserved something from the game.
"We've done the basics well, at 1-1 I thought we were in command. I thought Reuben Reid caused us a lot of problems, he was a constant source of aggravation for our back four.
"Football finds out if you have character, it doesn't give it to you. We need a lot of character now. This is a blow for us, but we've got 16 games to be better than the opposition."