Villas-Boas' men were outplayed by their visitors for much of Wednesday's Group C contest at the Stadion Petrovsky, with a strong performance from goalkeeper Yuri Lodygin ultimately keeping Monaco at bay.
Zenit did improve in the second half, but were unable to create any clear-cut opportunities on a frustrating evening for the Russian outfit.
Villas-Boas was under no illusions as to the shortcomings of his side.
"The first half was not the one we expected," he said. "We allowed Monaco to get a few chances, while we had a few in the second half.
"If we played both halves in a way we played after the break we could have got more from this game. That was a very tight tactical game as we expected."
Midfielder Viktor Fayzulin was also disappointed with the showing and felt Zenit made too many errors to claim all three points.
"We saw many battles in this game, while clear goalscoring chances were rare," Fayzulin said.
"Monaco are a very good team with much quality. They switched to defence very fast, while we too often had mistakes and lost possession.
"I think the coming [international] break will be very useful for us as we lack some freshness at the moment."
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