A bumper crowd crammed into the Falkirk Stadium after admission prices were reduced and the home supporters made their feelings known at the final whistle.
However, May insists he will not be paying too much attention to their reaction after being acclaimed following last week's win in Aberdeen, Falkirk's first at Pittodrie in over 50 years, that lifted them off the foot of the SPL.
May said: "They are allowed their opinions, they see things. It does not upset me, football is an emotional game and people are allowed their opinions.
"I think I was a hero last week and a villain this week so I will just take it as it comes.
"It's a long season, anybody that thought it was going to be an easy season needs to come into the real world.
"I've been on record about everything, it's a hard job but I was brave enough to take it on and we will see where we are at the end of the season.
"I didn't think there was much in it and the pitch didn't help at all. They have had two shots and scored, we have a shot and miss it. It changes the game."
Defeat to Kilmarnock, coupled with Hamilton's win at Dundee United, saw Falkirk slip back to 12th place in the league but May is refusing to panic.
He added: "If you're at the bottom you can only go up. We have another game on Saturday that we can climb off the bottom. It will change week by week and we will see what happens."
Falkirk started the brighter of the two teams but wasted chances through Marc Twaddle and Carl Finnigan.
Kilmarnock weathered the storm and an improved second-half performance was rewarded when Bryson latched onto Chris Maguire's pass in the box to drill a low shot past Robert Olejnik.
Kilmarnock supporters chanted for manager Jimmy Calderwood, who saw captain Manuel Pascali stretchered off after 30 minutes, to remain beyond the end of the season but the experienced coach refused to be drawn over his long-term intentions.
Calderwood said: "It's nicer than being booed to be honest. We are on a good run.
"Let's see, they might be booing in a month, I've been in the game long enough.
"The place was rocking when we came back against Dundee United and it was the same against Celtic. We have two home games coming up and it's great to have that kind of backing."
On the game, Calderwood added: "You're always happy when you win. We were disappointed with the start, we changed things a wee bit and they caused us all sorts of problems.
"I was really disappointed with the first half but we started to knock it about a bit and it was a wonderful goal."
When asked about being drawn with Celtic in the Scottish Cup quarter-finals, Calderwood added: "Don't spoil my night. It's a great night but a bad afternoon."
Source: Team Talk