The battling Bucks came from behind twice to earn a 2-2 draw and had a Ben Turner shot cleared off the line in the closing stages.
Jamie Ward then earned Buxton a point with a 66th minute leveller.
“We feel very disappointed we didn’t win the game,” said Cunningham. “If there was ten more minutes I think we would have won the game.
“We had to sharpen up in the second half and we did that, it may be a great point at the end of the season, but I’m disappointed we didn't get all three.
“Everyone keeps saying how good South Shields are and you will win the league if you finish above them.
“I thought we showed what a good team we are. Coming from behind twice shows character, especially when you look at recent results.”
Cunningham also felt it was a match in which Buxton had dominated the ball against their big-spending opponents.
“For a large part of the game we were the better team and if anyone deserved to win it it was us,” he said.
“The lads kept going and we got the ball down well. It was no surprise that the quality of football was there.
“We were the better team in the first half and for large parts of the second half.
“We gave them a head start which they certainly don't need. We didn't crumble, we carried on and showed great character.”