In remarkable scenes at Tynecastle on Saturday, Hamill scored the opening goal in the 2-0 win from the penalty spot before shoulder-charging the County manager Derek Adams, who had been complaining that the player's celebration involved running away with the ball.
Hamill, who was wearing the captain's armband in Wilson's absence, was swiftly shown a second yellow card and will now miss Sunday's visit to Easter Road to face Hibernian.
"Jamie has said he was sorry to the boys, but we're fortunate that we went on to win the game and it never really cost us," said Wilson. "It is not something we have spoken at length about; we will move on and it has been dealt with. It is one of those things and Hamill has the respect of everyone in the dressing room, so we don't feel the need to go on about it.
"It has been dealt with internally and by the SFA. I'm sure whoever comes in will do a good job and Jamie will learn from that."
It was believed that because referee Willie Collum dealt with the incident at the time, that the SFA could not take any further action beyond banning the former Scotland Under-21 cap from the derby match. However, the governing body's rules do allow for the compliance officer Vincent Lunny to intervene in cases of 'excessive misconduct' but it is not yet clear whether the governing body will increase the sanction.
Wilson acknowledges that Hamill's absence is "not ideal" for the derby, with Hearts' squad thin on the ground. However, recent meetings between the sides, as well as the clubs' contrasting current form, suggest the encounter will hold no fear for Hearts. Hibs are on a run of nine matches without a win, have lost their last five and have not scored in their last four outings, and are now within three points of a relegation play-off pace. Hearts have also won three of the four Edinburgh derbies this season.
"There have been a lot of times we have not done too well this season, but in the derbies we have turned up and put a performance on for the fans. That is something we are looking to do once more. Four derby wins will be a remarkable achievement. We have played well in these games."
Wilson is acutely aware that, having endured relegation for the first time since the 1980/81 campaign, Hearts fans would love nothing more than to see their city rivals dragged in to the Championship as well. But the defender is adamant he will not give the Hibs manager Terry Butcher any inflammatory headlines to pin up on the dressing room wall.
"We will just do our job as professionally as possible and we can only do that by going there and winning. Yes, that will pull them further down but that is not our priority. It's not for me to say something to fuel their fire Whatever happens in the rest of the season with them is their issue."