Goals from James Hanson, Rory McArdle and Nahki Wells earned Bradford promotion to League One as the Cobblers were brushed aside 3-0, with all the goals arriving in the opening half hour.
Boothroyd told Sky Sports: "I think for 30 minutes we never performed. I thought Bradford's League Cup game here against Swansea might have worked against them but it certainly worked for them.
"They dealt with the whole day, the occasion, the game better than we did for 30 minutes. That's the disappointing thing for me, it's such a poor end to a really good season.
"It's not about being overawed, it's about making sure you think correctly when the pressure is on, and do the right things at the right time and I didn't recognise a lot of my lads out there for half an hour today.
"It was, for one or two of them, too much, but I do have to say they've been absolutely outstanding all season and the mark of a team, the mark of any individual is how quickly they bounce back and I know with this group we'll bounce back."
On the goals Northampton conceded, Boothroyd added: "It is (frustrating), we didn't win a first contact, we didn't win a second contact.
"You know against people like Wells and Hanson you are going to have a problem and we knew what was coming, we've played them enough, we've prepared for it. We dealt with it for 60 minutes but the game was over, the game was done.
"We tried and pushed and tried different formations but at the end of it, it came down to being able to do what was required in those situations and we didn't.
"It's difficult to do this. Nobody wants to be here and get beat but my players and staff have been brilliant this year, absolutely fantastic. We've come a long way. We are not winners today but we are winners and we'll be back."