The Latics' captain gave the 21-year-old his blessing after his transfer to the Blues, as his side proved they could win in his absence with a 2-0 victory away at Southampton
The 21-year-old Nigeria international completed a move to the Blues on Friday for a fee believed to be around £9 million after playing a key role last season, scoring six goals as his side secured Premier League survival with a late run of form.
"Vic has moved on after a great few seasons at the club," Caldwell told The Guardian.
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"He is a young player with fantastic potential and we wish him all the best and we hope he does really well at Chelsea.
"But we have to move on and this is an opportunity for other players to come in and keep the club moving forward."
The Latics won their first game after Moses' exit, goals from Franco Di Santo and Arouna Kone sealing a 2-0 victory at Southampton and Caldwell was happy to have picked up a win, and kept a clean sheet.
"We are delighted with the win. We came here with a game plan and real desire to win the match," the Scotland international explained.
"I thought after the first half an hour where Southampton played well and threw a lot at us, we really dominated the game. We got a goal at a good time and controlled the rest of the match."
Roberto Martinez’ side were defeated 2-0 by Chelsea at home in their first match of the season, and Caldwell insists his team-mates can take lessons from losses to the bigger sides.
He commented: "I think we tried to learn from last week. Last week we played a match which was over within seven minutes.
"We wanted to focus on being competitive and staying in the game. I thought we did that great. For Southampton, it was their first Premier League game at home and they threw a lot at us.
"We saw that period out and once we got the ball I think we dominated the game."