Boyd told BBC Tees: "Everybody expected us to come in and just run away with the league.
"But there's not many teams that have done that over the years."
Boyd added: "It probably gave everybody at the club a wake-up call.
"We're not quite ready to walk on a park with a swagger and think we're just going to turn up and win games.
"We need to turn and work hard. That's the only way you're going to get three points in this league."
Listen: Kris Boyd talks to BBC Tees (BBC iplayer)
The former Kilmarnock and Rangers striker started the match alongside his old Gers team-mate Kevin Thomson and ex-Celtic players Willo Flood, Scott McDonald, Barry Robson and Stephen McManus.
He believes their collective experience of collecting silverware with the Old Firm - as one of seven former Old Firm players - and the unique pressure of playing for one of the big two in Glasgow - will help bring a winning mentality to the Riverside.
"In Scotland when Rangers and Celtic are playing you can win 10 games in a row then draw one and when you draw one it's a crisis," Boyd continued.
"You do get that winning mentality and hopefully with the boys coming down here we can help the players here get that.
"But when you look at the squad at Middlesbrough there are players in the dressing room who have already won stuff in their careers as well so they know what it's like as well."
The Teesside club followed the defeat with a League Cup win against Chesterfield and drew a blank in their second league match, a 0-0 draw away to Leicester City.
And the 27-year-old says the overall performance was a marked improvement and is confident of opening his scoring account.
"For me it's been a difficult start because I've not really contributed a lot in the games," Boyd said.
"I felt from the first week to the second week a bit of improvement.
"When I look back to the game last week there was a couple chances that maybe three or four weeks down the line, if I was sharper, I might have tucked away.
"You can train for as long as you want over the summer but its games where you get your match sharpness and fitness and I'm sure the more games we get together then the better the team will be."
And he believes too much is made about how teams line up on the pitch.
"People make a fuss out of formations," he says, "I think formations are there as excuses.
We've both had an understanding of each other and you earn respect for each other from how hard it is to do the job of putting the ball in the net Kris Boyd on his partnership with Scott McDonald "It seems to be that whenever there is a European Championships or a World Cup every team wants to play the winner's formations. Teams haven't got players to play that way.
"At the end of the day eleven people cross that line they need to go and win a game of football.
"I'm sure once the manager gets the team settled and we start clicking we'll not be far away."
Such droughts were a rarity for Boyd north of the border, as the Scotland international overhauled former Celtic, Manchester United and Barcelona striker Henrik Larsson as the all time leading goal scorer in the SPL last season, and has seven international goals to his name.
The move to the Riverside renewed acquaintances with a former rival in new strike partner McDonald, who remains third on the SPL list.
However Boyd insists there will be no battle with his former Old Firm rival to become the club's top marksman this season.
"We've both had an understanding of each other and you earn respect for each other from how hard it is to do the job of putting the ball in the net," the forward continued.
"Hopefully we can work together and get Middlesbrough promoted.
"It should be a Premier League club but at this precise moment in time it's not, we all work together to thrive to get to the Premier League."