The striker was shown a red card two minutes after coming on as a second half substitute.
Fallon left the park in the 70th minute after being dismissed by referee Willie Collum following an elbow on Michael Hector.
The Dons opened the scoring thanks to Peter Pawlett's 17th-minute strike, while Niall McGinn added a second goal five minutes from time.
Wright said: "I think he's better staying out of my way. He hasn't come to me saying he hasn't done anything so I take it from that 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 but has channelled it in the wrong way.
"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."
As for the match, he added: "I don't think there was much between the teams.
"We are disappointed. A misplaced pass gave them the opportunity to score the first 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."
Aberdeen manager Derek McInnes added: "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."