"Just to clarify, I will always aspire to be great. I haven't reached that point in the NFL but that's what we all chase and I'm going to continue to work to help the Browns become great. Never meant the Browns are the new Patriots or going to be the new Patriots. I just have great respect for what they've done but definitely recognize the work that has to be done to get there," he wrote.
He added that the Patriots' success is what every player aspires for.
"There is nothing wrong with having aspirations, and who wouldn't aspire to be part of an organization that is 12-4, 11-5 and in the playoffs and playing for Super Bowls on the regular. It's really stating the obvious when you say you want your organization to be successful like the Patriots. I know my teammates want to be a part of building something like that, (head coach) Freddie Kitchens and (GM) John Dorsey are doing everything they can to get us there. Understand it doesn't happen without work and we're all committed to that," he wrote.
"Our work will determine what the Browns become," Beckham wrote. "I'm content with that because I know we control the amount of work we put in. I will keep working, working towards building something great!"
The star wide receiver made his comments on Monday to GQ, which chronicled his trip to the Met Gala. Beckham also told GQ that his new quarterback, Baker Mayfield, is "going to be a Hall of Famer."
The Browns have made the playoffs only once since returning to Cleveland in 1999 but were 7-8-1 after selecting Mayfield No. 1 overall last year, a remarkable turnaround from their 0-16 season in 2017.