The 20-year-old frontman was the hero for Tommy Wright's men when he struck the crucial equaliser against Norwegian's Rosenborg in the second-leg of their second qualifying round clash.
His goal secured a score draw in Perth and confirmed a 2-1 aggregate win that sent the former Champions League quarter-finalists spinning out of the competition.
But there was no place in the starting line up in Grodno as St Johnstone followed that victory up with another impressive display against Belarusians FC Minsk.
Steven MacLean grabbed the headlines with his 68th-minute winner, while May had to settle for a late run out after replacing Nigel Hasselbaink.
But now the forward hopes to down Hearts at McDiarmid in Saints' opening Scottish Premiership fixture of the new term and ensure he is in the Wright's plans for the return with Minsk.
May told Press Association Sport: "I was gutted not to be playing on Thursday night. But that's obvious. Ask any player who misses big games and they will tell you they are disappointed.
"But it turned out to be the right decision so there's no arguing with it. We all trust the gaffer. I'll just get my head down and hope to play in the next couple of games.
"Thursday will be a massive game for the club and the town and I want to play my part. Sunday is good opportunity for me to stake my claim."
May also believes the match against Gary Locke's administration-hit Jambos side will be no walkover.
He said: "Hearts have still got a lot of good players and they will bring a big travelling support with them. That will make it a tougher game than normal but we are quietly confident we can get the result."