Tring started sharply and, after five minutes, debutant Graham Clark picked out Adrian Fontenelle who smashed the ball into the net to put Athletic 1-0 ahead.
Tring carved out two chances to put the game to bed, but they were wasteful in front of goal and only had the solitary goal to show for their efforts at half-time.
The hosts were made to pay for their profligacy after the break as Berko hit back with an equaliser after 78 minutes.
There was still time for late drama, however, as Tring were awarded a penalty in the 90th minute.
Ben Seaton stepped up but smashed the ball over the bar as the game finished all square.