The veteran cornerback rejoined the Dolphins after they gave up a franchise-worst 517 yards passing by New England's Tom Brady in the season opener Monday.
Allen was back on the practice field 11 days after being cut at the end of training camp.
"This is a business," he said. "You've got to understand. You can't take anything personal. You take the punch, and you keep rolling. Bitterness doesn't get me anywhere, so here I am."
A 38-24 loss to New England prompted the Dolphins to bring back Allen. He was slowed by a hamstring injury at the end of training camp, which contributed to the decision at the time to keep Sapp instead, coach Tony Sparano said.
"One guy was healthy. The other guy really wasn't," Sparano said. "Allen's better right now."
Allen started 53 games for Miami from 2006 to 2009, then missed last season with a knee injury. Teammates in the secondary said they were glad to have him back.
"It's huge," safety Yeremiah Bell said. "He's a veteran guy who knows the game. He's a leader back there."
"You've always got something to prove," Allen said. "Always. I've felt like that since I set foot in this league, probably since I came out of the womb."