Heath was shown two yellow cards during the defeat at Bramall Lane yesterday, the first after tugging at Neil Shipperley's shirt, the second of the same incident only this time on Steve Kabba.
Adams said: "I've seen sendings-off and people getting booked like that before and perhaps my player could have been a bit more careful with his challenges.
"But if people start getting sent off for that, the game's gone. I thought it was weak refereeing because I saw people from Sheffield United having a chat with him [Webster] at half-time. That's my line and I don't want to say anymore on the subject.
The Sky Blues had taken the lead after 24 minutes when James Scowcroft fired home from eight yards after being supplied by on-loan Midfielder Willo Flood.
The former Foxes manager also went onto say "We have a tendency to press the self-destruct button at this club and we've got to start making the right decisions and taking our chances.
"It was always a tough ask with 10 men and we just didn't get there."
Three minutes after that City goal the Blades hit back and were rewarded with a goal when Steve Kabba slammed the ball past Stephen Bywater after being put through by Alan Quinn.
For once Blades boss Neil Warnock kept his mouth shut about his opinion on referee Mr. Webster but did make comments about the win; "I don't comment on referees, never have done," said Warnock, with more than a hint of irony.
"It's a squad game and we're going to need all our squad all season. We were limited with the subs but I thought Steve Kabba took his goal well and his general play was good. Neil Shipperley made Kabba's job easier because I thought Neil was dominant.
"We've got more quality on the bench this season and we've a little bit more variety because we've had a bit of money to spend in the summer. Everyone's mucking in and that's good."
The game was won by the Blades when Quinn was fouled in the box on 89 minute, David Unsworth stepped up and sent Bywater the wrong way to fire United to the top of the league!
"I couldn't look when he [Unsworth] took the penalty but you could see his quality." The former Bury boss staked his comments about the winner.
"He has an aura and about just oozes confidence because he's been in the Premiership all his life. It's been a good signing for us and it augurs well for the season.
"You're either or a hero or villain in the last minute like that and I'm glad he's a hero."