The Cobblers currently find themselves third from bottom in League Two - 10 points off the top seven - and were knocked out of the FA Cup by Sheffield Wednesday on Saturday despite an encouraging second-half display.
Beckwith told the Northampton Chronicle & Echo: "We have to start picking up our results in the league, and our aim is still the play-offs. That said, the first target is to get out of the bottom half and we can't really look any further than that because of where we are in the table.
"I think we've performed well in some games but haven't picked up the wins. The spirit in the camp is good. I think the second-half performance against Sheffield Wednesday proved that. Everybody is together."
On this weekend's crucial home match with Stockport, who currently sit two places and one point above Town, he added: "Every game is tough and Saturday's against Stockport is going to be a bit of a six-pointer.
"It's going to be a hard game. But I think we have the team and squad to win it. It is a young squad but we have some older pros like Andy Holt and Marcus Hall who give us experience and good advice."
Source: PA
Source: PA