Reds beat Blyth Spartans 2-0 on Tuesday night to record a sixth straight win in all competitions courtesy of goals from Jake Simpson and Scott Allison.
The hosts have also gone more than 450 minutes without conceding a goal and have cut Blyth’s lead at the top to five points.
Despite tightening their grip on second place, May believes his team must not get carried away.
He said: “It was very pleasing, not just to win against Blyth, but the way we played. We can do it against good teams.
“The fans have said that we need to add to the squad and you can only do that if you’ve got the financial backing.
“We’re five points off, which makes it interesting. It would be over with a 10-point gap, but we won’t get carried away. There will be a lot of twists and turns and teams will drop points.”
May has played in every game in 2016 so far and Reds’ only defeat this year came against Colwyn Bay on Saturday, January 2.
Reds beat Marine 2-1 in the reverse fixture in December and the teams will meet again in the League Cup later this month.
Gari Rowntree is doubtful for the game and Matty Tymon is still injured.
May added: “We will just have to play the way we have been playing. The start is key for us. We didn’t start well against Hyde, but we got away with it.”
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