Elsewhere, Anna Meares claimed her fifth Commonwealth gold as she won the 500 metres time trial to move level with fellow Australian Bradley McGee as the most successful track cyclist in the Games.
Wiggins, the 2012 Tour de France winner who was left out of this year's edition by Team Sky, had pinned all his hopes on the track event after opting out of the road race and the time trail.
But he, Ed Clancy, Andy Tennant and Steven Burke were well beaten at the Chris Hoy Velodrome by Jack Bobridge, Luke Davison, Alex Edmondson and Glenn O'Shea who won in a time of three minutes 55 seconds.
It now seems unlikely the 34-year-old Wiggins, who has now won four Commonwealth silvers, will ever add the gold to his long list of honours.
"We had limited preparations for this and hopefully we will look back in two years with gold medals around our necks thinking 'this was the starting point in Glasgow'," he told the BBC, referring to the 2016 Olympics in Brazil.
"I've said all along that the track was always what I was going to go back to," added Olympic time trial champion Wiggins. "I need to put some muscle on and get stronger.
"It's going to be two years of graft and we can't underestimate how much work we have ahead to get in the right place for Rio."
The 30-year-old Meares, Australia's flag bearer at the opening ceremony, clocked a Games record 33.43 seconds in the 500.
Compatriot Stephanie Morton took the silver while England's Jessica Varnish grabbed bronze.
New Zealand snatched gold in the team sprint final with a time of 43.18 seconds, beating an England team that included Olympic champions Jason Kenny and Philip Hines.
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- Anna Meares
- Andy Tennant