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.
"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."
"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."
