Saints forward Gregory Tade was dismissed in the 38th minute with his side already 1-0 down to a well-taken John Sutton penalty.
But Hearts could not capitalise on their advantage until the closing stages when David Templeton slotted home, although McGlynn reckons his side were better over the course of 90 minutes.
He said: "I think overall yes, I definitely do (deserve the result). I have got to be happy with that, we have kept a clean sheet and scored two goals and it was an entertaining game for the fans.
"I have to give St Johnstone a lot of credit and a lot of praise because we were 1-0 up and they had 10 men and he sticks another striker on and goes with a 4-3-2 formation.
"We lost our way in the second half and that is always a possibility when you're playing against 10 men."
Tade was shown a red card after seemingly raising a hand during a scuffle in the penalty area with Andy Webster, but McGlynn thinks that the sending off made the job harder for his players
"I personally hate playing against 10 men," he said.
"We were doing perfectly well when it was 11 v 11 and we were in control. We got a bit slack and they thrived on that and created us problems, one that we cleared off the line and another that was saved by Jamie MacDonald."
In his first game in charge of the Jambos, McGlynn started with two teenage full-backs in Kevin McHattie and Callum Paterson and he was delighted with their contribution, confirming 17-year-old Paterson will start the Edinburgh derby against Hibernian next weekend.
"If he is fit he will play next week," McGlynn said.
"There are not many people who would fling two full-backs into a back four going into an SPL encounter but we've given them experience in the pre-season friendlies - they have settled in tremendously well.
"They (McHattie and Paterson) played their part in their home debuts in front of a big crowd that could have put them off but they handled the situation perfectly.
"They have played in a back four, kept a clean sheet in an SPL game and won the game and I think this will stick in their memories for years to come.
"We have these guys and a few more behind the scenes - that is a good sign ahead for the Scottish international team as well."
St Johnstone boss Steve Lomas had no qualms with the decision to send off Tade and labelled the striker's actions 'stupid'.
"The sending off is not in debate, Gregory is stupid," he said.
"Of course there is a club punishment, you can't go around doing that. I've made mistakes myself in the past and Gregory will have to learn the hard way, obviously it hurt us but I would rather focus on the positives."
Despite the defeat Lomas felt his side were in the ascendancy during the second-half and could have travelled back to Perth with a positive result if they had taken one of their chances created whilst on top.
"I thought we played very well in the second-half, I thought we were the better team and we had three great chances at 1-0," he said.
"I commend my players for the positivity in the second half, especially the first half an hour. I asked the boys to stay in it as long as we could and we would get chances. We did but we didn't take them."
