Spurs battled hard at White Hart Lane to hold off the Toffees, leapfrogging the Merseyside club into fifth place, in a match vital for their top four hopes.
Emmanuel Adebayor scored the only goal of the game in the 65th minute and that was enough for Sherwood to praise his men after a tense affair in north London.
"We're delighted with the result," he told Sky Sports.
"Yeah, the performance can be better but it's about character - grinding it out when you're not playing well - and a lot of the games are going to be like that. It was chalk and cheese between the first and second halves, but in the end we've come out on top.
"I asked them to put some pressure on higher up the field. We were standing there admiring them - let's get up and at them. I didn't want too many gaps between the midfield, but we were too deep with them. We had to push them on, and work as units, and still have our threats on the counter.
"It was huge, it was a cup final. I don't want to rubbish our performance - but sometimes people win cups when they haven't played very well."
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