The final positions had already been decided in Group C, with City qualifying second behind Barcelona and Celtic finishing bottom.
City manager Pep Guardiola will, however, have been keen to bounce back from Saturday's 3-1 Premier League defeat to Chelsea and a 3-3 draw in Glasgow earlier in the season that started a six-game winless run in all competitions for his side.
But it was one of City's own who put Guardiola's men on the back foot inside four minutes at the Etihad Stadium, Roberts - on an 18-month loan at Celtic - capping a determined run with a powerful finish.
Another City youngster – this time wearing the blue of the hosts – soon levelled, Kelechi Iheanacho rounding off a swift counter-attacking move.
The pace of the game started to reflect its dead-rubber status as it wore on and Nolito's rightly-disallowed goal was as close as either side came to snatching a winner in the second half.
With nothing riding on the match, Guardiola used the opportunity to give some of his fringe players game time, bringing Tosin Adarabioyo into a defence that almost instantly came under pressure thanks to a loose Fernando pass.
That ball was pounced on by Moussa Dembele – scorer of two goals in the reverse fixture – before Tom Rogic forced a retreating Willy Caballero into an early save.
The opening goal came after Caballero asked a lot of Leroy Sane with a chipped pass out to the left wing.
Germany international Sane did enough to keep the ball in play but it was collected by Mikael Lustig, who sent Roberts on a driving run into the box that ended with a smashed left-footed effort beyond the City goalkeeper.
Celtic's lead was short-lived, Iheanacho powering a strike past Craig Gordon four minutes later after getting on the end of a precise Nolito throughball.
Iheanacho then fired just wide as City looked to complete a rapid turnaround, but Celtic remained a threat at the other end, Dembele smuggling the ball past Caballero only to find the side-netting with a wild swing.
It was City who looked most likely to edge in front before the break - Erik Sviatchenko turned behind a dangerous Nolito ball into the six-yard box, before Gordon got down well to keep out a clever Iheanacho flick.
A Gael Clichy tug on an advancing Roberts went unpunished in the closing stages of the opening half, but chances were at a premium in the early stages of the second.
Substitute Jesus Navas created the first real opportunity with a low cross from the right in the 66th minute. Nolito put it in the back of the net, but he was correctly flagged for offside.
Celtic replacements Leigh Griffiths and Gary Mackay-Steven both went close for the visitors late on - the former sweeping wide from the edge of the box, before his team-mate was denied by a strong Caballero hand.
But there was to be no winner and Brendan Rodgers will no doubt be the happier of the two managers, with Celtic avoiding defeat on their travels for just the fourth time in Champions League history.
Key Opta stats:
- Kelechi Iheanacho has scored 13 times in 18 starts for Manchester City.
- Celtic's two quickest Champions League goals have both come against Man City this season (2:23 and 3:51 in this match)
- Manchester City are unbeaten in their last eight Champions League home games (W5 D3), their longest run without a defeat in the competition at the Etihad.
- Celtic are winless in their last nine Champions League games, which is now their longest run without a victory in the competition.
- Celtic have finished the group with three points, their joint-lowest tally in a Champions League group (same as 2013-14). This is the first time they've failed to win a group game.
- Tosin Adarabioyo became the youngest Manchester City player to start a Champions League game (19y 73d).