May's side ran out 1-0 winners thanks to Colin Healy's superb strike after 31 minutes. The three points moved the Bairns off the bottom of the Scottish Premier League table on goal difference and May was delighted to end his side's long winless streak in Aberdeen.
He said: "It is a nice feeling to win a football game, especially to finally win here after over 50 years. It is a big thing.
"I think we are off the bottom just on goal difference so it shows you that there is a thin line between success and failure. I thought we deserved to win tonight and that isn't being disrespectful to Aberdeen.
"Aberdeen will be a very good team under Mark (McGhee) but I thought tonight we had a couple of chances to kill the game. Their 'keeper had a couple of good saves. They had a lot of pressure near the end but I thought our boys from the back to the front were excellent."
The Falkirk boss was thrilled on-loan Irishman Healy chose the match to score his first for the club and expects the midfielder to add to his tally by the end of the season.
He added: "Colin has struck the ball like that a few times at training. It is great that he can get forward and strike the ball like that. I thought we created a few chances tonight and I'm grateful that we got the three points because I think they will be a very, very good team under Mark McGhee."
Aberdeen manager Mark McGhee admitted his side did not play well enough to win.
The Dons boss handed new loan signings Steven MacLean and Jim Paterson debuts but the pair failed to prevent their new side slumping to their fourth defeat in their last five home league matches, while Zander Diamond was also handed his first start since the opening day of the season.
McGhee said: "We played poorly at the back and although it was a new back four I'm not going to use that as an excuse for why we played poorly at the back.
"Individually we didn't cope well but Zander was probably the best of the back four and he hasn't been playing all season. I wasn't too disappointed with Jim Paterson either, he looked like he needed the game. I think our defensive performance undermined the rest of it and it got untidy."
McGhee said the performance of MacLean, who has signed on loan from Plymouth Argyle until the end of the season, was one of the few positives he can take from the match.
He added: "Steven held the ball up and I thought he did well. He showed us what he can do which is link the play and he has a composure on the ball that gives you time to get people up around about him.
"He was a whisker away four or five times from getting people in on goal. One of these times he is going to create a chance for someone like Gary McDonald or Darren Mackie so I was pleased enough for him."
Source: Team Talk