Centre-back Cresswell and right-back Clohessy were included in the end-of-season XI at the PFA awards, with only promoted sides Gillingham, three players, and Port Vale, two, earning similar recognition.
Cresswell has enjoyed a memorable debut season at Roots Hall following his switch from Rotherham, finding the net eight times, while right-back Clohessy has played every minute of all Southend's 59 games this season - with the pair featuring in Southend's Johnstone's Paint Trophy final defeat to Crewe at Wembley.
The accolade comes after Clohessy was named as the club's Supporters' Player of the Year, coming after he also scooped the Players' Player of the Year award.
He told Southend's official website: "It's nice to receive the recognition from fans who are obviously pleased with how I have performed this season. I must say a big thank you to everyone who has voted for me.
"As a player it's always great to be appreciated by supporters so to have won both the Player of the Year awards is fantastic and I'm delighted.
"I'd say it has probably been my best season that I've had. My role has changed a lot this season because the year before it was about supporting Ryan Hall and almost letting him do his own thing.
"This season I've worked well with Kevan Hurst and Gavin Tomlin down the right and we've got some joy from it. I think I've performed pretty consistently throughout the season, it's just a shame as a club we're not getting promoted or getting ready for the play-offs."