First-half goals from Cameron Stewart and Johnnie Jackson had looked to hand the Addicks their third away win of the season, but a Michael Morrison own goal and Ishmael Miller penalty earned the Somerset side a point.
Charlton had captain Johnnie Jackson sent off with 12 minutes remaining for a foul on Luke Ayling but Yeovil could not capitalise.
Glovers boss Johnson was left frustrated with his side's poor performance in the first half and said Yeovil must improve to secure Sky Bet Championship safety.
Johnson said: "We had opportunities to get more from the game but we didn't show enough intent in the first half. It took us to be 2-0 down before we got going.
"The overall quality wasn't good enough. I'm pleased we've come back to draw but it was an opportunity missed because of our poor start. We can't do that in the Championship as teams get the momentum and it's hard to wrestle it back.
"I think their first goal came from our corner and that's what teams can do at this level. They suck you in and hit you on the break.
"I'm pleased we didn't lose and the boys did show character, but if you show that character in the first minute then you won't lose many football matches.
"Everyone wants me to be happier than I am, but maybe my standards are high. If we're getting out of trouble we need to show that intent for 90 minutes."
Charlton manager Chris Powell said it was "two points lost" for his side and was disappointed with referee Craig Pawson's decision to send off Jackson.
Powell said: "Momentum swings happen in football, you see it time and time again. We were good in the first half, went in front with a classic counter-attack goal and our captain put us 2-0 up.
"They say 2-0 is a dangerous score but I thought we coped with that at the beginning of the half. The turning point was Simon Church's chance which would have put us 3-0 up.
"We were looking good but then conceded a deflected goal, and Yeovil had their tails up after that.
"We knew it would be a difficult game because of the way Yeovil have been playing recently, but in the end it's a point shared but perhaps two points lost from our perspective.
"I've seen the red card again and the referee has to make an instant decision. The player is not in danger and it wasn't over the top.
"He will now be suspended and it's a blow to be without him because he brings goals to the team, as he did today."