The Welsh striker, who is returning from injury, was brought on in the second half of the 1-0 defeat by Ross County, replacing Kevin Nisbet after 66 minutes, but was shown a straight red card on 84 minutes after a challenge on David Cancola.
Boyle, meanwhile, was given his marching orders after the final whistle following a confrontation with referee Gavin Duncan.
Asked for his take on both red cards afterwards, club captain Hanlon admitted he was surprised by both dismissals.
"At the time I was shocked. I never saw anything in [the Doidge challenge] at the time and play was going on and I didn’t think it was an incident worth focusing on, if you know what I mean.
"I didn’t think there was anything in it so I just followed the ball and, although I haven’t seen it again, it did seem harsh at the time.”
Boyle is understood to have commented on the referee’s performance, incurring a sending-off but again, Hanlon – who heard the remark – was stunned by the reaction.
“I was pretty close to the situation and I heard what he said and although I won't repeat it, I can say I didn’t think it merited a red card – nowhere near it – so we will have to see what comes of it now.”
Hibs now face a daunting trip to Perthshire to take on St Johnstone – whose manager Callum Davidson witnessed the defeat at the Global Energy Stadium on Wednesday night – and could be without Boyle and Doidge as well as Kyle Magennis, Dan Mackay, and Jamie Murphy, severely reducing the attacking options available to Jack Ross.
The Easter Road side will be looking to bring an end to their five-game losing streak when they pitch up at McDiarmid Park and avoid another frustrating 90 minutes.
Hanlon continued: "We came into the game full of confidence after the weekend but it was a strange game. I felt we were in control and didn't feel like we were going to concede a goal and if anyone was going to score, it was going to be us.
"We had a few decent chances and, although I wouldn't say anything was a bad miss, they were still decent chances.
“I felt we would kick on in the second half and go on and win the game but it didn't turn out that way and it has ended up as a really frustrating night.”
Doidge’s dismissal was a cruel blow with the striker still working his way back to full fitness after a lengthy spell on the sidelines and Hanlon admitted his red card was a turning point.
“It was disappointing to lose Christian when he had just come on – it was 0-0 at the time and we were trying to win the game, but it is a case of looking forward now.
"We need to recover as much as possible. The gaffer and the medical staff are doing all they can to help us with that but this period is going to be huge and there is no time to rest so we have to dust ourselves down and try to get the win on Saturday.
“It definitely is tough. It is about getting back on track as quickly as possible but if we are going to be missing players through suspension, like we were tonight as well, with Ryan [Porteous] out, then that makes it more difficult for everyone.
"We need to be more careful in these situations because we know this is going to be a busy period and we need everyone fit and available, firing on all cylinders and ready to go, so we need to be a bit more clever in these situations and not give the referee those kind of decisions to make.
"We have a tight squad and we can't afford to lose key players. That is something that we all need to be aware of. We will need all our best players available and playing in the games coming up.”
Wednesday night’s disappointment may have diluted some of the enjoyment from Sunday’s Premier Sports Cup semi-final win but Hanlon is adamant the Capital club can turn things around.
“It is still early in this run and we know it is going to be a tough run, but we have had a decent break because of the Covid-19 outbreak and then the international fixtures as well,” he continued.
"So, we are still fresh and ready to go in terms of Saturday. There is no doubt that it will be a taxing period between now and the end of December but we are still at the start of the run so we are fresh and ready to go.”
Hanlon also backed Kevin Nisbet after the striker missed a handful of chances but suggested the rest of the team perhaps needs to contribute more in front of goal. The skipper saw one effort around the half-hour mark smack the base of the post while Boyle also had a couple of opportunities.
"All credit to him because he still gets in those positions to have the chances,” Hanlon said of his team-mate.
"I missed a good chance in the first half as well and probably should have done better. It is a team game and we all need to chip in and try to score.
"We have probably been a bit too reliant on the same people scoring the goals and rather than focusing on Nizzy not scoring we should maybe focus on the rest of us weighing in a bit more.”