Craig Mackail-Smith cancelled out Lawrie Wilson's opener before substitute Kazenga LuaLua earned his side a point via a deflected free-kick.
"A point is all right," said Poyet. "I'm not saying I'm happy but I will take it.
"Sometimes you need to accept that things happen for a reason, like our second goal. I was absolutely mad about how close the wall was from the ball and we scored.
"Maybe if they had moved the wall three yards back we would have hit it in the stands.
"The only problem we had was that we had to chase the game all the time. When you go down 1-0 you have to chase and you make mistakes.
"Then we scored and it looked like we had the game under control but we made a mistake and had to do it again."
Poyet also revealed he was now back on speaking terms with his teenage son Diego - a youth-team player on Charlton's books - after a pre-match domestic squabble.
"He was very nervous," he said. "It was a difficult week for him. The only thing he asked me was `behave - don't do anything silly, don't get sent off or in any fights'.
"I did my job and I can go back happy."