Terry announced he was quitting the England team on Sunday, the day before his FA hearing into accusations he racially abused QPR defender Anton Ferdinand was scheduled to start.
Terry denies the charge, but felt he had no choice but to retire after the FA made his position "untenable" by stripping him of the England captaincy for a second time in anticipation of the court trial into the same charges.
Walcott said that none of Terry's England team-mates were aware of the decision before it was announced, but that the players and manager Roy Hodgson should look to the future.
"It came out of the blue, to be honest," the Arsenal winger said. "You've got to respect JT's decision. He's got other things going on at the moment so we've just got to respect it."
Walcott, speaking at the launch of the FA and Mars Just Play Free for One Week initiative, added: "We've just got to move on. We've got some great players that will come in."
Terry was first named England captain by former manager Steve McLaren just after the 2006 World Cup, a tournament which saw Walcott receive a shock call-up at the age of just 17.
Now 23 and with 29 England caps to his name, Walcott praised Terry for the role he played at the start of his international career.
"He was great to me when I first came into the team," Walcott said. "He will be missed - he's a great player."
The FA and Mars are offering a week of free Just Play sessions from October 8th. Search online for Just Play.