Papelbon, 27, was one of a group of 18 arbitration-ineligible players who came to terms with the Sox on Thursday.
"Of course they could have [renewed me without reaching an agreement]," he said. "I don't think any team wants to renew guys. It doesn't look good. It just doesn't look good. I didn't want to renew, either.
"I want to help this organization look good and I want to help this organization go out there and win championships. That's what the whole goal is here, and that's the whole thing I try to keep in mind. At the same time, you've got to go to work and produce championship teams year after year after year. I plan on being here for a long time and I plan on winning a lot of championships here."
While he acknowledged he is relieved the process is over, Papelbon said he understands the team's stance and is looking forward to next year, when he will be eligible for arbitration.
"Of course I'm looking forward to [arbitration]," he said. "That's what I've put myself in a position [to do]. Believe me, I understand that these guys have the upper hand right now. These are the guys that drafted me. These are the guys that put the time, the effort into it, that recognized my talent and gave me the opportunity to play. I understand that right now they are the ones that have the upper hand, so to speak. I understand the process, and hopefully they understand that I'm going to play this year out.
"Next year will be a little bit different scenario."
Since taking over the closer's role in 2006, Papelbon has 72 saves, becoming the first Boston pitcher to earn at least 30 saves in two seasons and the second Major League pitcher with at least 35 saves in each of his first two campaigns.
"I feel a certain obligation not only to myself and my family to make the money that I deserve but for the game of baseball," Papelbon said Tuesday. "[Yankees closer] Mariano Rivera has been doing it for the past 10 years, and with me coming up behind him, I feel a certain obligation to do the same."
Papelbon was believed to be seeking a one-year deal closer to the $900,000 contract the Phillies' Ryan Howard signed in 2007. Rivera re-signed with the Yankees in the offseason for three years and $45 million.
"Rivera was the one that has kind of set the tone from the beginning, 10 years ago," Papelbon said.
"Hopefully I can follow in his footsteps and do it for the next 10 years to come, when he's out of the game.
"I think the role of a closer is just now beginning to erupt and people are starting to understand how important a closer is to a ballclub -- especially a ballclub that wants to go win a championship. I think Rivera was the one that set the tone and established how important it is, and I feel it's my job to go and do the same and carry on that tradition. Hopefully I can do that."
When asked if he would be willing to give up free agency if it meant signing a long-term deal, Papelbon replied, "Now you're getting into next year's Spring Training. I don't know. Right now, I'm going year to year and we're going to see what happens. I can't predict what's going to happen in the future, man."