All three new boys played their part in ensuring May's rejuvenated outfit shocked Celtic by plundering a 1-1 draw from Parkhead - their first point won in the east end of Glasgow in 23 years.
Monday night's Scottish Cup exit at the hands of relegation rivals Kilmarnock was a disappointment, even though Falkirk were without Showunmi and Healy, as well as suspended pair Darren Barr and Carl Finnigan, who scored against Celtic.
However, May reckons similar displays to the one his new-look team put in against the Old Firm title hopefuls will be good enough for Falkirk to ease away from trouble.
He said: "The draw with Celtic gives the players confidence. It's not easy going to Parkhead and getting a result - it is 23 years since we last got a point.
"So I think they deserved it and the players should take a lot of confidence from that.
"In my opinion, we should have won the cup game. We just missed chances, good opportunities came along and we just didn't take them.
"That was disappointing, to go out of the cup, but we are fully focused on the league and we always have been.
"I'm delighted with the way the new signings have settled in. They're not here for the money, they're here to play football and they've shown that in their performances.
"If they can play to the level I know they can then we've got a very good opportunity to get off the bottom of the league by the end of the season.
"Some players will play well and some won't but as long as the team functions in the right manner that's the most important thing.
"If we can get that throughout the rest of the season we've got a fantastic opportunity to get off the bottom of the league."
Dundee United arrive at Westfield with uncertainty still surrounding the manager's post since the departure of Craig Levein to the Scotland job.
Levein's assistant, Peter Houston, remains in place as interim boss but has ruled himself out of the running for the job, despite steering the Tannadice outfit to three successive wins.
May is focused on his own team, however.
He added: "I know Peter Houston and I've known him for a number of years, and hopefully he does a very good job until someone else comes in there.
"But we've improved enormously since we were beaten by them 2-1 earlier in the season and it's about what we do on the day.
"If we can play to our strengths and get a bit of luck then I'm sure we can get points out of the game."
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Source: Team Talk