The 28-year-old, signed during Spurs' summer spending spree, had scored six goals for his new club going into the Europa League Group K dead rubber against the Russian outfit, but had not found the target since the 1-0 Barclays Premier League win over Hull on October 27.
However, the former Valencia forward, who has been dealing with his wife losing their baby, showed on Thursday just why the north London club splashed out £26million for his services.
Speaking after the 4-1 European victory, Soldado, who had posted a picture of a positive pregnancy test on Instagram in November, said: "A month ago she was pregnant, but unfortunately she had a miscarriage and lost the baby, so now, well, that is that.
"They (his family) have been here tonight and I've really enjoyed their support at the stadium. My family feel fine and are settled - so am I. The only thing missing were the goals and they've come along (on Thursday night) so let's hope that from now on they keep on coming."
Spurs boss Andre Villas-Boas has previously hailed Soldado for how quickly he settled into his new surroundings, but the Spain striker conceded it had been tough.
"It's true that the first couple of months are quite difficult," he said.
"There are a lot of changes to be made, and as soon as you leave training you have a lot of things to sort out - school for the kids, a house... but things have all been very stable for a while now so I've been able to concentrate solely on football matters and what I needed to be doing, and that was scoring goals, and (against Anzhi) I've managed to do that."
Tottenham return to Barclays Premier League action on Sunday when they welcome Liverpool to White Hart Lane.
A victory would move Spurs level on points with Brendan Rodgers' second-placed side and Soldado wants to see an action replay of Thursday night's performance.
"That is what we all want - to have 30 points on the board by Sunday," he said.
"It's going to be a difficult game for us. We all know what sort of potential Liverpool have as a team, but we are at home and we need to be strong and go for the win by going out with the same attitude (as Thursday night) - go all out for the three points as that is the only way that the team will get the victory that we all want so much and those three points that would push us further up the table."
Despite Soldado's hat-trick heroics against Anzhi, Villas-Boas has refused to rule out dropping him to the bench and bringing back Jermain Defoe for the Liverpool match.
With a packed festive schedule over the next month, the Portuguese is keen to utilise all of the players available to him to keep things fresh.
"The Christmas period is something decisive in England," he said.
"It is nothing different from the past, but, due to the demands of the game and the intensity of the game right now, only big, big squads can survive this period because injuries can happen and setbacks can happen.
"We have most of the squad fresh apart from the players who are drained because of the international fixtures.
"Those are the ones we have been more careful with. We have given more days off to players who have been over-charged, like Paulinho and Kyle Walker - it is something that we have to be very sensible about."