Juventus forward Cristiano Ronaldo (L) reacts next to teammate Federico Bernardeschi after receiving a red card during the UEFA Champions League group H football match between Valencia CF and Juventus FC at the Mestalla stadium in Valencia on 19 September, 2018.
Valencia's last game in the Champions League was Gary Neville's first as manager and there have been four more in charge since.
German referee Felix Brych did not have access to a video review but showed a red card after consulting his assistant behind the goal.
"I can only say that VAR would have helped the referee make the right decision", Allegri said.
"It is disappointing because we will lose an important player for at least a match".
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Ten-man Juve rallied and took the lead on the stroke of half-time when Miralem Pjanic scored from the penalty spot, and shortly after the break, the Bosnian midfielder stroked home another spot-kick.
Valencia were even awarded a third spot-kick of the match deep into injury-time but Daniel Parejo missed.
Juventus face Young Boys in Turin next, on October 2, before back-to-back games against United and Allegri feels his side have put themselves in a strong position.
Jose Mourinho's men were inspired by Paul Pogba on the artificial pitch, as the French World Cup victor drilled home a brilliant opener before converting a penalty on the stroke of half-time, and setting up Anthony Martial for the third.
City trailed by two goals at halftime, when errors were punished by Maxwel Cornet and Nabil Fekir, a member of France's World Cup squad.
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"Ronaldo will serve a one-match ban but anything more would be harsh".
"It could have complicated the situation for us, but the guys have been very good". "If you give cheap goals away it is hard".
Bale nearly increased Madrid's lead with a close-range shot that struck the crossbar early in the second half but the Wales forward did make it 2-0 in the 58th with a well-placed low shot after a superb through ball from Luka Modric.
After leaving the pitch the five-times Champions League victor, whose stoppage time penalty for Real Madrid knocked Juve out in the quarter-finals last season, waited by the tunnel entrance, seemingly on the verge of tears.
Bale added the second after a brilliant Luka Modric pass, with the Welshman lashing home brutally to double the score.
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However, these two teams will both be favourites to progress from Group G, which also contains Czech side Viktoria Plzen and CSKA Moscow.