The sides couldn’t be separated as it ended 1-1 on the Kent coast.
A Kevin Lokko own goal put Pools ahead but Dover battled back to take a share of the spoils when lively Nassim L’Ghoul scored late on.
Both midtable sides are hoping to build up enough momentum to push for the top seven in the weeks ahead.
But Challinor thinks nobody will be over the moon after just claiming a point in the only National League game of the weekend.
He told the Hartlepool Mail: “A point does no team any favours really.
“If we had been absolutely horrific and scraped a point then a much as I’d be disappointed, it would feel like a point gained.
“At the moment, because of how we’ve done in the game and the manner of the equaliser and how late it came, it feels like a loss.”