The forward believes Hoops fans should be worried as Brendan Rodgers’ team are lacking confidence and an alternative plan.
Celtic slumped to sixth on Sunday following a 2-1 defeat at Kilmarnock and their 10-point total after six matches represents their worst start to the season for 20 years.
The departure of Moussa Dembele in the final hours of the transfer window left Celtic without the sort of powerful striker that Boyd feels successful teams need.
Boyd told talkSPORT: “Only Rangers fans will demand that they come out and take Celtic on and go head to head with Celtic. The rest of the clubs know that there is a way to play against Celtic now.
“We’ll sit in, we’ll frustrate them. We know if you give Celtic space in behind when they’ve got pace, they’re going to hurt you.
“But if you make the pitch as narrow as you possibly can, drop off and let Celtic have the ball, it’s very, very difficult for them to break you down, because they don’t have that big strong physical striker that a lot of successful teams do.
“And Brendan won’t change it. You don’t need to go back that long – Jan Vennegoor of Hesselink, you had (John) Hartson and (Chris) Sutton and you could throw the ball into them. Celtic don’t have that right now.
“If they don’t play through you, if they don’t cut you wide open, then they’re going to struggle to score.
“Teams understand how to play against Celtic and they’ve not got that confidence where they’ll try things because the Celtic players look as if they’re scared to give the ball away.
“It’s going to make it an interesting league now because Rangers have definitely turned the corner.”
Boyd claimed Scott Sinclair typified the lack of confidence in the Celtic ranks.
“Scott Sinclair looked a pale shadow of the player he was, it was actually pretty sad to see – no confidence, didn’t want to take anybody on,” said Boyd, who was an unused substitute on Sunday.
“When you’re confident, you look to get on the ball. He was the opposite. He was trying to hide behind defenders and didn’t want it.”
The late win moved Killie above Celtic on goal difference, one point behind second-placed Rangers and six behind leaders Hearts.
“We’re in a good place, we have got ourselves back into contention now,” Boyd said.
“We feel we can cope with the majority of teams in this league and if we perform to the level we did on Sunday, especially second half, then we can be a handful for anyone in the league.”