The hosts somehow managed to ride a first-half storm and took full advantage when Emmanuel Adebayor's scored what proved to be a decisive strike after the interval, showing impressive skill and strength to control the ball before firing home following a quick free-kick from Kyle Walker.
Sherwood, though, acknowledged that his men cannot expect to go unpunished if they continue to ease their way into matches.
"I keep finding myself coming in and saying the same thing," he said. "We started slowly again and we have got to find out the reason why.
"Hugo Lloris has kept us in the game again early on and made some great saves, one especially.
"But we sat them down (at half-time), had a little chat and decided that we needed to put some more pressure on them higher up the field, which was the gameplan originally.
"So in the second half we stepped into them a little bit, made them play quicker and they gave us the ball back."
The result means Tottenham jump above the visitors into fifth spot, behind Liverpool in the race for a Champions League spot.
Martinez, meanwhile, was left wondering how his left White Hart Lane without anything to show for their endeavours.
His frustration was heightened when Everton looked to have a strong penalty claim turned down, after substitute Etienne Capoue caught Seamus Coleman in stoppage time.
"I think we started the game really, really well," said the Spaniard.
"It is fair to say at times in football you are better to be lucky than good and today we played the good role, not the lucky one.
"But I thought from our point of view the only criticism about the first-half performance is that you need to hit the back of the net with the chances we had."