The captaincy has since passed on, with Dutchman Glenn Loovens leading the team in Tuesday night's 1-0 defeat at Kilmarnock, where new signing Robbie Keane made his debut in attack.
Celtic had no Scotland-eligible players in their starting line-up for the game, although Scott Brown and Paul Caddis both came off the bench.
Collins said on BBC Radio Five Live: "As a manager and a supporter you would always want the spine of your team, your key players, to be local lads and to come through the system.
"That's the ideal scenario.
"Celtic fans love nothing better than to have a local hero but at the same time they love a superstar foreign player, ie Henrik Larsson.
"I'm sure they're working behind the scenes looking for the next young Scottish player that's going to lead the team.
"That is what they're missing: a real leader on the park to galvanise the team and drive them forward."
Rangers, the defending Scottish Premier League champions, hold a 10-point lead over second-placed Celtic who have Hibernian chasing them, two points behind with a game in hand.
Collins is convinced Keane will enjoy plenty of success during his loan spell from Tottenham, which runs until the end of the season, but he recognises Celtic have left themselves with plenty to do over the remainder of the season.
Discussing Keane, Collins said: "He's a good football player, there's no doubt he'll bring something to Celtic.
"He'll score goals in Scotland without a doubt.
"But they're 10 points behind now, it's going to be a long hard slog."
Former Hibernian boss Collins also suggested new Scotland manager Craig Levein would like to see more Scots on show at Celtic.
"Unfortunately it's going to have an effect on the national manager," he said.
"It makes his job so much more difficult heading along to Celtic Park and no Scottish players being on the park."
Celtic 1/4, Draw 4/1, Dunfermline 9/1