It was not the ideal start to a group that also includes Bayern Munich and Red Star Belgrade.
Megson was confirmed as Bolton's new boss earlier on Thursday to widespread condemnation from the majority of Trotters fans.
He had been Leicester manager for only six weeks after previously being unable to revive Nottingham Forest's fortunes.
Archie Knox took charge of his second and final match against a Braga side that had finished fourth in the Portuguese League last season.
In a very dull first half, Kevin Davies had Bolton's best chance to break the deadlock with a header after good play by Nicky Hunt while Braga had little to offer in attack.
The second period was little better until El Hadji Diouf's introduction. The controversial former Liverpool star had only come on to the pitch as a substitute three minutes earlier when he got on the end of Davies' 66th minute cross to head home at the far post.
Jussi Jaaskelainen was forced to make a tremendous save to deny Paulo Cesar Peixoto an equaliser but it looked as though Bolton would be able to hang on for a sketchy victory until Braga launched an 87th minute attack.
Alves dos Santos Jailson was able to loop a header over Jaaskelainen as the match ended all-square.
With his side at the foot of the Premier League table, and struggling to adapt to the post-Sam Allardyce era, Megson has a tough task placating the Bolton fans and improving life at the Reebok Stadium.