Spurs started slowly, showing signs of a hangover from their 5-1 drubbing at the hands of Manchester City in midweek, and the Tigers duly capitalised when Shane Long latched onto Nikica Jelavic's flick-on to fire his side into the lead.
But the visitors came on strongly after the interval and Paulinho, who made his much-anticipated return from an ankle ligament injury, netted a well-deserved equaliser while Vertonghen also returned from a spell on the sidelines to help marshall the defence and ward off the threat of Long in the second half.
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"Vertonghen as well, I thought he grew into the game as it went on. Younes Kaboul was on the bench there and there's a few coming back to full fitness.
"By the time we play Everton next week we won't be too far off full strength."
Sherwood also credited Hull's two club-record signings after seeing the newly assembled strikeforce wreak havoc in the Spurs backline, particularly early on.
"They've got threats," he said. "Obviously the two new signings up front. [Shane] Long gave us a problem early doors chasing lost causes and he took his goal very, very well."
Hull boss Steve Bruce was only too quick to lavish praise on his new signings and, having seen them fire blanks at Crystal Palace in midweek, the Tigers manager was delighted with their response.
"He gives us something that, certainly since I've been here, we've been missing," Bruce said when quizzed on Long's performance.
"He gives you that pace and once he gets through, the you know he's going to run away from everybody but I thought him and [Nikica] Jelavic were a handful for Tottenham all day long and once we turned the ball over and got it forward to those two I thought they caused problems.
"His goal summed it up, he got the flick-on and burst through. He will give us what we have been lacking before.
"I'm looking forward to working with them over the next few months because they're a handful, that's for sure."