Dons boss Mark McGhee was disappointed with letting slip a win so late in the game.
"I thought we deserved to win the game and we're very disappointed not to have," he told BBC Radio Scotland.
"That was a chance to maybe finish above St Johnstone missed, but we'll keep going and try to catch them.
"Coming here as depleted as we were, the players showed a great attitude to try and win the game. Our shape and determination were excellent."
McGhee added: "Sometimes you feel you need a second a goal, but I didn't particularly feel that.
"I thought we were solid enough at the back and we were never really threatened, although St Johnstone have a physical presence.
"I thought that we dealt with that, especially considering the players we had missing."