With Saints trailing to Peter Pawlett's 17th-minute strike from long distance, Wright threw on Fallon in the 70th minute but he was shown a straight red card by Willie Collum for an elbow on Michael Hector just over 60 seconds later.
St Johnstone had struggled to break down a resilient Aberdeen defence other than in one first-half moment when Jamie Langfield saved brilliantly from Stevie May, and the numerical disadvantage proved too much as Niall McGinn doubled the lead with a superb curler with five minutes left.
Wright had not seen footage of the incident before speaking to the media and when asked if he had spoken to Fallon, he said: "No, but I think he's better staying out of my way.
"We have to see it but he hasn't come to me saying he hasn't done anything so I take it from that the referee has made the right decision.
"But we will see the footage and we'll deal with it in house if we feel that the decision is right. Everyone I have spoken to indicates it is the right decision.
"He has been sent on to give us a bit of aggression. He has channelled it in the wrong way if that's the case.
"That kills the game for us. We could have a right go in the last 20 minutes but going down to 10 men, it was always going to be a really uphill task to get back in the game."
Wright added: "I don't think there was much between the teams. We are disappointed with how we passed it in the first half. A misplaced pass gave them the opportunity to score the goal. It's a good strike from Peter but it takes a deflection.
"We have a good chance to get back into it and Langfield makes a great save. The second half was pretty even. We are ready to push on in the last 20 minutes and we got a sending-off."
Aberdeen manager Derek McInnes, who was making his first competitive return to his former club, said of the flashpoint: "I have just seen it again there, just once, and I think there is a raised elbow there. Only Rory Fallon can tell if it was deliberate or not and in the referee's eyes it was."
McInnes, who lost Ryan Jack to a calf injury late on, felt his side were deserved winners despite the helping hand from Fallon, who left Pittodrie in the summer.
McInnes said: "We knew we would get chances to produce some quality and bring composure to the game in the last third and the two bits of quality for the goals were outstanding, two terrific goals.
"But that alone didn't win the game. It was all the fundamentals - the headers, the second balls, winning individual battles.
"All in all I think we were worthy winners. The sending-off took the wind out of St Johnstone a wee bit and helped us get over the line."