Luck has missed the past two games with a right shoulder injury.
"It was good," Luck said. "Another step in the right direction."
It's uncertain how much Luck and the Colts actually practiced Monday because the media was not permitted to watch. Pagano also would not definitively say whether Luck will play Sunday, referring to the quarterback as "day-to-day."
When asked if he could play a game if the Colts had one Monday, Luck said, "I don't have to play a game today, so I'm not going to answer that."
Luck is 0-4 in his career against the Patriots, losing by an average of 29 points. New England beat the Colts 45-7 in last season's AFC Championship Game.
"This is certainly a big game, it's the next game," Luck said. "It is a very, very good team that's undefeated coming to town, and there is certainly a history between us and them. But it's also a new year, and you have to take care of business at home."
If Luck can't play, veteran Matt Hasselbeck will start his third straight game at quarterback. Hasselbeck has led the Colts to back-to-back victories by going 48-of-76 for 495 yards and three touchdowns in his two starts.