McLaren subsidiary MES (McLaren Electronic Systems) mandatorily supplies electronic control units to every team in F1.
A new unit for 2013, in preparation for the radical new V6 engine rules next year, caused several problems in recent winter testing.
But Martin Whitmarsh, the McLaren team principal, said earlier this week that Red Bull could have been responsible for the Melbourne glitch.
"You can also inflict ECU problems on yourself by how you set it up, but I will look into it," he said.
That investigation has now been done, and McLaren subsequently apologised to Red Bull in a media statement.
The Woking based company admitted there was a "software-related issue" with Webber's unit.
"That disrupted his preparations for the start of the race, for which Mark and the team has our apology. We are working together with them to prevent any recurrence," said McLaren.