Soldado had not scored in the Barclays Premier League since netting the winner against Cardiff on March 2, while it had been 593 minutes since he had last scored in competitive action.
So it was something of a relief for both Pochettino and Soldado that the Spaniard latched onto Aaron Lennon's pass before coolly slotting the ball past Tim Howard and into the far corner to give Spurs victory.
"You need to give confidence to the player to keep working hard," Pochettino said of the former Valencia front-man. "It has not been easy for him but you need to motivate the player - it is always frustrating for a striker who does not score.
"Today he scored and he is happy, he is more free because he feels the pressure.
Tottenham Hotspur 2 Everton 1 - Player Ratings
"It is important for the team that the striker scores goals."
It looked to be another miserable afternoon at White Hart Lane after Kevin Mirallas' superb goal had given the travelling Toffees the lead in the 15th minute.
Having already lost at home four times this season, Spurs fans must have been fearing the worst but Christian Eriksen struck six minutes later before Soldado grabbed what would turn out to be the winner on the stroke of half-time.
Pochettino has previously questioned the mental toughness of his team but the Argentinian was delighted with a hard-fought victory.
"Our mentality and our spirit were fantastic," Pochettino said.
"This is what we want. We need to keep this feeling. It is impossible always to win but with the spirit and mentality we showed, it will be easier to win games."
He added: "Everton have a very good squad and for us it is not only three points, it is a little bit more than three points.
"It is important to grow and build on the victory."
Spurs were fortunate not to concede a late penalty when the ball struck Federico Fazio's arm as the defender jumped in the air to meet a cross.
Pochettino believes referee Michael Oliver was right not to award a spot-kick but Everton boss Roberto Martinez disagreed.
"I'll never blame a decision like that for not getting a result, it happens, it's part of the game," Martinez said.
"But I'm disappointed because Michael Oliver is a really good referee and when the ball contacted the arm he wasn't in an obstructed view and I think it should have been spotted. It was a real shame."
He added: "I would never blame a third party for us not getting a result though. We should be good enough to come to White Hart Lane and get a result."
Everton were without influential midfielder James McCarthy for the contest.
The 24-year-old is struggling with a recurrence of a hamstring injury and Martinez admitted the club will "take a bit of time" before bringing him back.