Northampton had gone three weeks without a game and were only back in training this week due to an outbreak of COVID within both the squad and playing staff.
Initially, that did not show in an entertaining first-half against Swindon with Sam Hoskins hitting back for Cobblers after Harry McKirdy's opener.
Jon Guthrie then steered the visitors in front five minutes after half-time but McKirdy immediately equalised before Northampton fell apart.
Swindon scored four times in 15 minutes to take full advantage of an extremely rusty and sluggish Cobblers outfit.
"We needed a game and we were desperate for a game because 21 days is a long time without one," said Brady.
"There were some players out there who trained for the first time yesterday due to COVID and I had three on the bench that there was no way they could come on today.
"A couple of players only joined the group on Friday so to have them start the game, it's very tough on them, but we had to do it because we have to get the momentum of playing games again.
"Your timings off and your awareness is off for certain things and it was very hard to get good preparation in for the players.
Swindon have also been disrupted by COVID but they were able to play against Stevenage in midweek, whilst the Cobblers had barely trained as a full group.
"The players were nowhere near conditioned," Brady added. "Of course we know we have to defend better but your distances and your awareness would obviously be much better without the break.
"I'm not going to make excuses today but I'm just telling you where we are as a group because it's been tough. We haven't had the whole group together - the first time was yesterday.
"It's been very stop-start with everybody but we will be better for this game and it was important that the subs got a good run-out as well."