The former Ireland goalkeeper departed for Championship side Leeds shortly after Hoops manager Mark Hughes completed the signing of the England international on a free transfer.
Kenny was forced to apologise after sending abusive text messages to QPR chairman Tony Fernandes and technical director Mike Rigg criticising Green’s performance in QPR's opening day 5-0 defeat at home to Swansea, in which the first goal resulted from his error.
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"We have only had two games. He has the ability so we just leave him and give him the confidence."
After notifying Leeds of the messages, the west London club did not demand any further action, and Park commented: "We have not spoken about that.
"He is not a young player and has experience. Every player speaks to each other and if we have problems we sort them out.
"He is not worried about them, and showed that he is getting better."
The Hoops recorded a 1-1 draw away at Norwich on Saturday, and the former South Korea international commented: "The most important thing is we did better than last week. It was our first away game and we got a point.
"We are working in the future to get better. Everyone knows we have ability but we need to improve a lot."
The club are expected to add defensive reinforcements in the remaining days of the transfer window before taking on champions Manchester City away on Saturday, having attempted last week to sign centre-backs Michael Dawson from Tottenham and Ricardo Carvalho on a season’s loan from Real Madrid.
Meanwhile, midfielder Joey Barton, two matches into a 12-game ban, has been heavily linked with a move to Marseille.