The black, green and gold had lost four successive league matches and seemingly slipped out of contention when they were beaten at Gloucester on March 5.
But since then they have produced a stunning revival, claiming 32 points from the 35 on offer, racking up six bonus-point wins in their past seven matches.
They scored 10 tries as they saw off Newcastle Falcons on the final day at cinch Stadium at Franklin's Gardens, earning a hugely entertaining 65-26 win that secured a top-four finish.
And Boyd said: "A couple of months ago we were sitting eighth or ninth and we had a lot of work to do to get to where we've finished up.
"I'm very proud of the way the boys have played in patches in the last period of time.
"We've been playing knockout football for the last little bit and to come through in fourth spot is very pleasing.
"I thought we did some really good stuff, some lucky patches but we were dreadful in that period after half-time so we clearly got the half-time message wrong.
"But to get a good bunch of tries in the game here, in front of our supporters is very pleasing."
Saints will play at Leicester Tigers next Saturday after Steve Borthwick's side finished top of the regular-season table.
And Boyd said: "I hear we're going to Leicester and we knew if we'd managed to get into the play-offs that was the most likely place.
"Our two worst performances this season have both been against Leicester so we'll be trying to turn that around."