The Royals looked destined for a 1-0 loss at the Madejski Stadium before Adam Le Fondre's last-minute penalty rescued a point.
With trips to Chelsea and Sunderland next up before the international break, McDermott was delighted to avoid the prospect of going into the next home game in a month's time yet to get off the mark. "It's a strange thing to say but, psychologically, it's important that we got that result today," he said.
"We know we can compete. We've done that today - there's no doubt about that. So it's important to get a result and we have got a result today."
McDermott insisted a draw was "the least" his side deserved.
"We'd have been disappointed to have lost the game over the 90 minutes," he said. "Those of you who have seen Reading play over the last three years know that they keep going. We have scored a few late goals in our time."
Stoke boss Tony Pulis was left fuming at referee Kevin Friend's penalty decision.
Pulis felt the verdict itself - which also saw midfielder Dean Whitehead shown a second yellow card - could have gone "either way". But he was more angry about Friend's decision to play advantage, allowing Reading a shot at goal, before deciding to pull it back.
Pulis said: "I'll speak to [referees' chief] Mike Riley on Monday and find out how long they're going to give. They either play on or they call it back.
"It gives the advantage to the attacking team, so it's a good rule. It's just being consistent. Where does it start? Where does it end?"