The Spain international converted his third penalty of the season with just 10 minutes remaining to seal an uncomfortable 1-0 win after Ahmed Elmohamady had been adjudged to have handled Jan Vertonghen's cross.
The victory took Spurs back in to the top four and Soldado hailed all aspects of the side as they look to develop in to a squad capable of winning the league.
"We're doing well at the moment," he said.
"We had to keep up with the teams who won on Saturday and Chelsea won as well, so we had to keep up with them.
"Apart from the blip against West Ham I think we've done very well at the back recently to not have any goals scored against us and I think we've done well, we've won our game and we're moving forward."
The penalty was a contentious decision by referee Michael Oliver that left Hull boss Steve Bruce fuming at full-time.
Alex Bruce made his Premier League debut in the Hull defence at White Hart Lane and agreed with his father's assessment of the penalty.
"When you work as hard as we did at a place like White Hart Lane to come away with nothing and get the decision go against us like we did, it is disappointing," he said.
"At the time I thought it was so soft and I had a good view of it.
"I always think that if a player puts his hands above his head then he is being a bit risky but he didn't have his hands there, they were chin height if that.
"The crowd, 38-40,000 people, and they are all screaming for a decision it obviously must be difficult for a referee.
"You don't ask for any favours but you have to ask if it was at our end would we have got it?"
The 29-year-old Bruce was utilised alongside fellow central defenders Paul McShane and Tigers' captain Curtis Davies as the visitors set up with a 5-4-1 formation.
After keeping the embarrassment of attacking riches available to Spurs quiet for much of the game, Bruce believes it is a system which could serve the top-flight newcomers well on their travels this season.
"We defended very well," he added.
"We had a game plan and we stuck to it. Tottenham, with the quality they have got, struggled to break us down and the only real attempt I can think of is the penalty. There are positives we can take out of it.
"It is an option we can look at when we go away from home.
"We were very solid and limited Tottenham to very few minor chances so we can take the positives and hopefully when we go away to the bigger teams in the Premier League we can go to that formation and make it hard for them."
The narrow defeat means Hull remain 10th in the table having collected 11 points from their opening nine league fixtures, with Bruce's side returning to White Hart Lane for their Capital One Cup fourth round tie on Wednesday night.