Babin told ESPN's "NFL Live" on Tuesday that his release caught him by surprise.
"Anytime your cell phone rings and it says Andy Reid, you know it's not good," he said.
He said Peyton Manning's release by the Colts last year proved that no player was untouchable, however.
"In the game of football, you can never be too sure of anything," he said.
Babin's release came after the team had earlier placed starting receiver DeSean Jackson on injured reserve with fractured ribs.
"We appreciate everything that Jason has given this team over the last couple of years. We wish him all the best as he continues his career," coach Andy Reid said in a statement. "By releasing him today, this gives us an opportunity to give more playing time to some of the younger guys in the defensive line rotation."
Babin, 32, had a career-best 18 sacks for the Eagles last season after re-signing with the team as a free agent two offseasons ago with a five-year, $28 million contract.
He had 5.5 sacks this season.
The Eagles fired defensive coordinator Juan Castillo on Oct. 16, but Philadelphia has actually performed worse under new defensive coordinator Todd Bowles. Philadelphia has allowed more than 30 points in four of the five games since Castillo's firing and 28 in the other -- all losses.
Babin said the Eagles' defensive struggles were a matter of execution and that Reid still had the respect of the Eagles' players.
"We were practiced hard, coached well and we just didh't execute as a whole," he said.
Babin sounded confident that he will soon find a new NFL home.
"I like to win, I like to compete and I like to sack the quarterback. I imagine there's a team out there looking for that," he said.