The Green & Golds had led Division 1 for all but the final week of the season and were pipped to the championship by 2012 winners Sarisbury Athletic.
Sarisbury Athletic clinched the title with a four-wicket win over Bournemouth, while New Milton brought down the curtain on their campaign with a tie against Basingstoke & North Hants.
Despite winning their first nine games – including a victory over Sarisbury – New Milton suffered a disastrous August which saw them lose three times against mid-table opposition.
Beck, who had skippered New Milton for three years and led them to third place in 2013, will stay on as a player and also in his capacity as club coach and committee member.
He said: “Had we been promoted, I would have done it for one more season and it would have been nice to have a crack at the top division.
“I have done it for three years and it is time for a change and to get in some new blood.
“We have the personnel, but possibly a change in attitude here and there might put us right up there.”
Beck, who confirmed vice-captain James Park was pondering an invitation to replace him, added: “We had a very good season and second is the highest we have ever finished.
“We threw it away on a couple of occasions but also won games we could have lost and vice-versa. We celebrated after the final game and didn’t commiserate.
“Sarisbury have been the best team in this division for the past three years and they deserve to go up. They are a good bunch and I would like to wish them well for next season.”
An all-too-familiar batting collapse cost New Milton after they had reached 104-5 in pursuit of Basingstoke’s 118-9 (Dan Loader 3-20, George Watts 3-21) with a scampered single off the final ball seeing the spoils shared (James Park 29, Nick Elliott 25).
Bournemouth, meanwhile, failed to poop the party at Allotment Road, losing by four wickets to a Sarisbury side which celebrated a second SPL1 title in three seasons.