Boss Dave Frecklington was furious over the second-half performance by Spalding United and the referee as a two-goal lead was thrown away against 10 men.
The Tulips looked in control as Bradley Wells marked his debut with a close-range double.
Bedworth United defender Kyle Cartwright had already been sent off but they fought back and levelled with only five minutes left following a controversial free-kick.
Frecklington – who was serving a touchline ban carried over from last season at Lincoln United – said: “The referee was an absolute disgrace.
“I’ve never seen officiating like it. You could see from half-time that he wanted to even the game up.
“He was inadequate for this level of football and he would not even let me go to speak to him after the game.
The referee was an absolute disgrace. I’ve never seen officiating like it. You could see from half-time that he wanted to even the game up.Dave Frecklington
“Matt Varley made a great tackle on the edge of the box but he got booked and they scored from that free-kick.
“But that was not good enough from us. We were miles away from where we want to be in the second half.
“The first half was perfect away from home, going 2-0 up against 10 men.
“We said ‘well done’ but they went out and couldn’t get the basics right.
“For one or two players, the game was a little bit too much for them.
“Pre-season is never a real indication. You have to see them in competitive games.
“I thought that Wells was absolutely superb. But at the end Tom Waumsley should have won it and if you are not in the team then you have to stake a claim.
“This is a ruthless division but credit to Bedworth who have it a right go in the second half.
“We made them look bang average in the first half and we should have got three points.
“We’ve got to win our home games, starting with Carlton Town on Tuesday night.
“Hopefully we will get a good crowd supporting us.
“We want to win the title. We didn’t come here to be a mid-table team.
“But Saturday’s second-half performance was miles away from what we want.”