Everton had by far the better of the first half and Tottenham were indebted to Hugo Lloris for pulling off an outstanding save to deny Leon Osman inside 10 minutes.
France goalkeeper Lloris had to pull off a number of other stops as Tottenham struggled to live with Everton's brisk passing and movement before the break.
Yet Tottenham improved in the second half and Emmanuel Adebayor's clinical left-footed finish secured a 1-0 win that ensured the hosts leapfrogged their opponents into fifth place in the Premier League.
Sherwood was at a loss to explain his side's lacklustre first-half display, but was pleased by the manner in which they responded to his instructions at the break as they enhanced their chances of securing a top-four finish.
He said: "I sat them down at half-time and said 'look, you're just waiting to get beat. If you keep stepping off these guys, they're good players, give them the time to play and they'll play and open up chances and you can't rely on your goalie to pull off saves all the time'.
"The tempo was higher (in the second half), our pressing was higher and that means we win the ball higher up the field and we looked a threat.
"The contrast between first and second half for me is encouraging, that they've took it on board, and we have to try and address it.
"I'm not really pleased with how we're starting games."
The London club are three points behind fourth-placed Liverpool and Sherwood knows his side are going to have to roll up their sleeves and grind out results as the battle to secure UEFA Champions League football hots up.
He added: "There's going to be fine margins between now and the end of the season and (that will decide) what takes the team into that fourth spot, which we're all chasing.
"More games are going to be grinded out like that one rather than free-flowing football and smashing people up three- and four-nil - that isn't going to happen."
