Second-half goals from Ivan Toney and top scorer Marc Richards, with his 18th goal of an injury-hit season, left the Robins a point adrift of safety with two games left to play.
Johnson, who had a brief but disappointing spell in charge at Northampton, admitted his side have it all to do to get out of trouble.
He said: “It was a poor performance, every player was below their standard and they showed they can’t put in two good performances back-to-back.
“Tuesday night’s win at Oxford gave us hope but if you don’t play with quality and the opposition do have that quality then you will get beat.
“Northampton is not an easy place to come, they’ve got some good footballers here and we didn’t get close enough to them. We need to be much better in our passing, in terms of getting the ball from A to B, that needs to improve, and we need to be more potent.
“We were throwing it around at times and we didn’t show any physical or mental strength. We know we just need to be better than two other teams, it’s as simple as that now.
“I would never get excited about us playing well for five minutes but we will do all we can to stay up. So my message to everyone is don’t slit your wrists just yet.”
Cobblers boss Chris Wilder was delighted with his side’s display.
He said: “We were very creative in the first half and made chances without being clinical enough. But we got the goals in the second half and ran out comfortable winners.
“They threw everything at us late on and had some chances which I was disappointed with because they shouldn’t have got anything today with the performance we produced.
“We’ve always managed to create chances but keeping the ball out of the net at the other end has been our problem since January.”
Wilder knows how costly the absence of top scorer Richards, who has missed two lengthy periods through injury, has been to his side’s promotion push and was full of praise for the striker who scored on his return shortly after coming off the bench.
He added: “Marc Richards tucks a goal away almost straight away after coming on. But that was a bittersweet moment for me because although it was great to see him back I just wish we could have had him back earlier.
“That’s taking nothing away from our other forwards, especially Ivan Toney who has been excellent in his last few games. He has got undoubted ability and will only get better but it shows how much we have missed Marc at crucial stages this season.”