The Royals went ahead in the 31st minute when Swans goalkeeper Michel Vorm allowed a Pavel Pogrebnyak shot to squirm beneath him and they doubled their advantage a minute before the break thanks to Noel Hunt's volley.
The hosts had been the better side in the opening half, though, and continued to press after the interval, with Michu's header reducing the deficit in the 71st minute before Wayne Routledge slammed home an equaliser seven minutes later.
Swansea were also thwarted by a string of excellent saves from Reading stopper Alex McCarthy and had claims that Nicky Shorey had handled in the box waved away by referee Mike Dean.
The drama then continued as Royals midfielder Jem Karacan had a 90th-minute header cleared off the line by Swans skipper Ashley Williams.
The final outcome meant McDermott's men are still without a top-flight win this term after six games but post-match, the manager was not complaining too much about a potential victory squandered.
"I know what happened in that second half," McDermott said.
"Our goalkeeper has pulled off some fantastic saves, Swansea played really well and that is a point gained for us.
"I couldn't tell you how many, but I do know he (McCarthy) has made some fantastic saves.
"So at 2-0, we have got to 70 minutes, but we are just sort of waiting for something to happen on their behalf.
"We need to affect the game better than we did in the second half. But having said that, that is a good point gained here."
That point - Reading now have three - did in fact take the Royals out of the relegation zone but asked about his side's league position, McDermott said: "I'm not overly concerned about that at the moment.
"Obviously it is good to climb up the table, but I just think that is definitely a point gained.
"I know we were 2-0 up and you would say it is an opportunity for us, and it is - it is certainly an opportunity.
"But I know that in each and every game we have been involved in, we've been in the game - apart from the Tottenham game where we got beaten 3-1 - so we'll take that today and move on."
Referring to Karacan's late chance, McDermott said: "That is us all over - we have done that for a long time now.
"For the last three years we have won games late on and we nearly won it in the last minute.
"It was a good clearance off the line. It would have been nice to get that winner, but we must not be greedy."
McDermott insisted he had not seen the incident involving Shorey, who blocked a shot by Pablo Hernandez.
"I'm not copping out - I genuinely didn't see that," he said.
"I didn't even know anything about that, so if that is the case, that is the case. I couldn't tell you one way or another."
Swansea manager Michael Laudrup was more certain on the matter, claiming the Welsh outfit had been denied a legitimate spot-kick.
"Who knows what would have happened if we got the penalty we should have?" Laudrup - whose team had lost their previous three matches in the Premier League - said.
"It should have been a penalty - obviously, it is football so you can't use your hands if you are not the goalkeeper. But the referee didn't give it and that is what can happen.
"It is a little difficult to say if it was a point gained or two lost - you can say both or neither."