Sarri has complained about Lazio's lack of additions this summer.
But Fabiani insists there is mutual respect between the pair, stating: "I have no regrets. Marriage is a two-way street; we chose each other. Let's downplay the headlines that have been made; the season will tell us about the transfer market's negative impact.
"The team has remained the same; it reached the quarter-finals, went out on penalties in Europe, was in the running for a place in Europe until the end. As the season progresses, we'll see if the transfer market has penalised us. I say no, there will be time to correct something, in January of course.
"Sarri is a playful man, a true Tuscan, and he wanted to stimulate the atmosphere and the dressing room. He knows what he's doing, no problems. We're only playing our second game of the season, and all games are tough. We've seen what happened on other pitches, like in Milan. Let's move forward with confidence and humility, which are the qualities we need to stand out with in this championship."
Fabiani was also asked about the prospect of re-signing Lorenzo Insigne, who is now a free agent.
He added, "Insigne in January? There's plenty of time between now and January. We won't be doing any transfer business until then. We won't be circumventing the rules, even if they needed a moment's consideration, but out of respect for the club and not to expose an entire fan base. Insigne or no Insigne, if there is a transfer window, it will be in January."