The reigning champions went into the Ligue 1 clash seven points behind early pacesetters Marseille, with Marcelo Bielsa's men facing a tricky trip to Lyon on Sunday.
Blanc's men suffered a major blow when defender Van der Wiel was somewhat harshly shown a straight red card in the 28th minute, giving third-placed Bordeaux the upper hand at Parc des Princes.
However, Bordeaux striker Andre Biyogho Poko followed Van der Wiel down the tunnel a few minutes later for a reckless challenge and PSG eventually took charge, with a pair of Lucas Moura either side of half-time putting them in command.
Ezequiel Lavezzi added the third late on to ensure the gap to Marseille was slashed to four points and Blanc felt Van der Wiel's red card spurred his side on.
"When you find yourself down to 10 it becomes complicated, especially when you've played a Champions League match in the week with a return at 6 o'clock in the morning." said Blanc.
"But actually, the sending off gave additional motivation to the team.
"But [I think we] would have also shown it [extra desire] with 11 [men]. I would have liked to see this match with 11 against 11."
Blanc was was not convinced that either player should have seen red.
"There are actions which deserve penalties, but before giving irrevocable sanctions there are yellow cards [that can be given]." said the PSG coach.
"On the two expulsions, the affected players continued to play. It is a contact sport.
"I would not be referee but playing an hour with 10 against 10; that's a lot."
