The black, green and gold shipped seven tries as they slipped to a sobering defeat at cinch Stadium at Franklin's Gardens on Saturday afternoon.
The only consolation for Saints was that they bagged a try bonus point thanks to two scores from Courtnall Skosan and efforts from Alex Mitchell and Alex Waller.
But it was nowhere near enough as Tigers ran out easy winners on enemy territory.
"They're at rock bottom and so they should be," said Boyd, when asked how his players were feeling after the defeat.
"It's the nature of professional sport and (it hurts) any time you get 50 points put on you, let alone by your derby mates.
"They are tough lessons for us and we'll have to work hard next week and go again."
Saints had won four of their opening five league games, but they were brought back down to earth with a real bump by a Tigers team who have now won seven from seven this season.
And Boyd said: "It's a tough day at the office - a big drop.
"We conceded way too much in the first half and then we clawed our way back into the game.
"They went down to 13 men and we had a couple of situations where if we'd have got a little bit closer it might have been a different game.
"We continued to chase the game and paid the price.
"No complaints really - we were the masters of our own destruction.
"Well done to Leicester - they're going very well."
Saints had fallen 27-0 down inside 35 minutes as Tigers raced to a try bonus point.
And Boyd, who was without his three full-backs, Tommy Freeman, George Furbank and Ahsee Tuala, added: "In the first bit, we dropped nine or 10 aerials.
"We knew exactly what was coming, and we didn't deal with it.
"We didn't win too many collisions so when you're not winning collisions and aerial battles, it's going to be a tough day at the office.
"We fought back well but didn't get it right when we had that advantage.
"We got a couple of tries but should have got a couple more."