Graham labelled the cautions as "crazy" and the Leeds manager was particularly unhappy with the Scunthorpe official's decision to award Leicester a penalty which Garry Parker converted in injury time of the first half.
Jimmy Hasselbaink, Leeds' pounds 2m signing from Boavista, blasted his own spot-kick wide of a post in the dying seconds to hand Leicester their first home League victory since October and take them within two points of Leeds.
"The referee had a bad game," Graham said. "You get a booking for just kicking the ball away. I thought his decision-making was bad, especially on players backing into opponents.
"Before the penalty there were three occasions when we should have had a free-kick. The referees don't understand that good centre-forwards can back in and get a lot of free-kicks when they are not playing the ball.
"Cottee and Heskey were backing in on a number of occasions. You could see Heskey was doing it on every opportunity he got in the box."
It was Heskey who earned the penalty for Parker when he was held by Gunnar Halle in the last minute of the first half. It looked a fair decision by the referee but Graham was unconvinced.
He added: "It's part and parcel of the game and if players can get away with it then good luck to them. I think the standard of refereeing is very very poor and most managers would agree with that.
"They have to enter into the spirit of the game. I think Uriah Rennie is by far the best referee in the country. He actually looks as if he is enjoying the game and gets into some dialogue with the players.
"When I was playing we had dialogue between the referee and players but nowadays they are like robots."
Goal: Parker pen (45) 1-0.
Leicester City: Keller; Savage (Zagorakis, 87), Guppy, Kamark, Elliott, Prior, Izzet, Lennon, Parker, Cottee, Heskey. Substitutes not used: Arphexad, Campbell, Wilson, Fenton.
Leeds United: Martyn; Kelly, Robertson, Haaland, Wetherall, Wallace (Maybury, 86), Hasselbaink, Ribeiro (McPhail, 86), Hopkin, Halle, Kewell. Substitutes not used: Bowyer, Matthews, Beeney (gk).
Referee: N Barry (Scunthorpe).
Bookings: Leicester: Elliott, Guppy. Leeds: Robertson, Kewell, Kelly, Wetherall, Wallace.
Man of the match: Heskey.
Attendance: 21,244.Reuse content