The Giants were well beaten by the Eagles, who progressed with a 38-7 victory at Lincoln Financial Field on Saturday.
Barkley recorded 10 touchdowns in the regular season, but made just nine carries for 61 yards against Philadelphia.
After a strong season for him and the Giants though, the 25-year-old said he wants to stay with the franchise "for life" despite his contract expiring this year.
"I don't want to jump to any conclusions. I've been vocal about how I feel and where I want to be," he said. "That's outside my control. I wanted to show the Giants, show them that the guy that they drafted is still here. I hope I did that.
"Everyone knows I would love to be a Giant for life, but I really can't give a 100 per cent answer. It's out of my control. Sometime this week, I'll get a conversation with my agent Kim [Miale] and see what's up.
"The way we played for each other this year, it was special. Obviously, it didn't end the way we would have wanted it to end. Not just because of the record or because we made it to the playoffs, this is probably one of my favourite teams of all time."
Quarterback Daniel Jones – who was sacked five times in Philadelphia – also sees his deal run out at the end of the season, and was less certain about his future intentions than Barkley.
"We will cross that bridge when we get there. I really enjoyed playing here," Jones said. "I appreciate all of those guys in the locker room. It is a special group of guys and I have really enjoyed being a part of it.
"We will figure out where that goes, but I have nothing but love and respect for this organisation and the group of guys in the locker room."
Coach Brian Daboll showed respect to the Eagles for their performance, admitting his team just second-best in every area of the contest.
"Give Philly credit. They did everything better than we did [Saturday]," Daboll said. "Tough game. We really got beat in all facets, so it wasn't one thing in particular. It was a team game, and we just didn't get it done. Congratulations to Philly. They get to move on, and unfortunately we don't."