But the 26-year-old, who arrived at Sixfields from Hereford last summer, believes much will depend on the opening weeks of the new campaign.
"Everyone knows we got off to a poor start last season," Beckwith told BBC Radio Northampton.
"But if we make a better start then I definitely think we have a good enough squad to get into the top three."
He added: "We've lost two or three players from last year but the main squad has been kept together."
Beckwith also paid tribute to the impact manager Ian Sampson has had on the club since taking charge last September.
"The gaffer came in when Stuart Gray got the sack and we had a good run from November right through to the end of the season," he said.
"We've worked hard together in pre-season and now we want to keep that momentum going."
Source: BBC Sport
Source: BBC Sport