The 20-year-old striker was magnificent for the Perth men in their 4-0 win over Inverness, scoring once and laying on three others.
It was the type of display that has already earned the seven-goal frontman Under-21 honours but May now wants to take a place in Gordon Strachan's full squad.
He said: "You've got to aim as high as you can and the full Scotland squad is my long-term ambition. But I've got to get myself into the Under-21 side first and maybe get a goal or two.
"You've got to work on your game and give your all every week and see what happens. Hopefully I can put in more performances like that and it will help me."
May spent the previous 18 months out on loan to Alloa and Hamilton before announcing himself as a fully fledged Saints player with a goal against Rosenborg in the Europa League qualifiers.
Now after helping his side pick up their first win since August 17, the striker wants to lead another charge for the continent.
"We've got to be hard to beat as a team and there's no reason why we can't be top six again and challenging again for Europe," he said.
"Every team will have ups and downs. Celtic will even have the odd loss but no-one else will be that consistent. Inverness have had a right good go at it but we have managed to turn them over. But if we can try and play like we did today as often as we can, we will be up there."
St Johnstone were slick as they passed their way round Caley Thistle on their way to an impressive three points.
May's opener saw the striker exchange passes with Gary McDonald before prodding home at the near post after 17 minutes as Saints got off to a flying start.
Another one-two combination from Dave Mackay and May then set up the right-back to double St Johnstone's advantage nine minutes later, while Tommy Wright's side were just as clinical with their exchanges in the second period as May teed up Steven MacLean to plant the ball in Dean Brill's bottom right-hand corner on 73 minutes.
And May notched up his third assist as he played in MacLean for his fifth goal of the season with a tap-in at the back post nine minutes from time.
The heavy defeat cost Inverness their place at the top of the Scottish Premiership table and goalkeeper Brill admitted he was left baffled by their lethargic display.
"It was a bad day at the office," he said. "It was a bit of a shock for us all. We didn't see that coming. We have been playing well but that's football. You are going to get a couple of these results a season but hopefully it won't happen again too soon.
"The manager wasn't happy after the game and a few honest words were said. But sometimes that needs to happen. He wasn't overly aggressive, just honest.
"But it came out of the blue for us. We didn't do anything different to our normal preparations but some days you are below par and get away with it. This time, we were punished."