Spurs moved up to fifth, level on points with fourth-placed Liverpool, after earning a 3-1 win at the Liberty Stadium thanks to a brace from Emmanuel Adebayor either side of a Chico Flores' own goal.
Wilfried Bony, who hit the bar, pulled a goal back with 12 minutes to go but Swansea could not get any closer as Spurs remained unbeaten in the Premier League under Sherwood since he took over from Andre Villas-Boas.
A delighted Sherwood said on Sky Sports News: "I thought we we played well, even though Swansea had some chances from distance in the first period and knocked it around, I thought we ironed it out and we got to grips with it.
"They are brave on the ball, they do pass when marked and credit to them for that, but we always thought that we could catch them.
"And even when they were having a lot of possession I thought we were the most dangerous side and it was just a matter of time before we clicked and found that final ball, and we did that many times in the second half and we could have gone on and won more comfortably."
On Adebayor, who has now scored six goals in eight games, Sherwood said: "It's great. It's obviously great for the football club and great for Ade himself, who's flying at the moment and enjoying his football.
"He plays with a smile on his face and he's finding the back of the net."
For Swansea, the defeat means they remain just three points above the drop zone and manager Michael Laudrup admits they have "some problems right now" .
However, the Dane was pleased with his side's attitude against Spurs and believes things could look a lot different once they get a win.
Laudrup, whose side have now gone eight league games without a victory, said: "Again, great attitude, put them under pressure, had a couple of good chances...and then the first time they have a shot on target they score.
"But it's something that happens when you're a team that is struggling a bit. It's not our moment and things like that happen.
"I think we have to admit that we have some problems right now, we haven't won for quite some time, but on the other hand we just have to continue like this.
"I think the only thing we need is a success, that means a win in the league, and now we just have to move on."