The Coasters started slowly at Mill Farm but finished strongly, scoring twice in the final 12 minutes to severely dent Sutton’s title hopes.
Challinor’s side know they have to keep on winning if they are to secure a play-off spot and the boss says they are a match for anyone when they’re at their best.
“I hate losing and I hate drawing so I was livid at half-time,” he told Fylde’s website. “To be fair to the lads they were equally annoyed because they knew they weren’t at it.
“I wear my heart on my sleeve and I tell them the truth. Sometimes the truth hurts but they showed me that they can do it in the second half and they deserved the three points.
“If we play the way we know we can – the way we played in the second half – then we are very difficult to play against.
“The games get bigger every week now, none more so than two long away trips to Torquay and Maidstone over the coming days.”
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