Tottenham maintained their challenge for a top-four finish when their only shot on target from Adebayor gave them a 1-0 victory over Everton in a Premier League match they were lucky to win.
Adebayor, frozen out by former manager Andre Villas-Boas until Sherwood succeeded the Portuguese in December, has now scored seven goals in the 11 league and cup matches he has played in since.
The striker's goal came after he controlled a quickly-taken free kick from Kyle Walker on his chest and held off two defenders before firing a left-foot shot into the bottom corner of Tim Howard's net.
"It was a cute free kick from Walker. Ade still had a lot to do but as soon as he put it on his left foot I knew it was going to end up in the net. I am delighted with him," Sherwood told reporters.
Even Sherwood said Spurs "were fortunate" to get the win that lifted them above Everton into fifth place on 47 points with 13 matches to play.
Spurs trail Liverpool, who are fourth, in the race for a Champions League spot by three points.
"We played far too deep in the first half and Everton opened us up but we upped the tempo in the second half and Everton never had a shot on goal," Sherwood added.
"It was chalk and cheese between the first and second half and there are going to be fine margins for the rest of the season to try and get that fourth spot and there will be more games like this one. We were fortunate to come away with the three points."
Following Liverpool's 5-1 demolition of Arsenal in Saturday's other clash between Merseyside and north London, neither team could afford to drop points.
"I said before if you want to finish fourth you have to pick up the points from the teams around you so today was not too bad," said Sherwood. "And we also beat Manchester United at Old Trafford."
Everton coach Roberto Martinez said he was still wondering how his team lost.
"Sometimes in football it's better to be lucky rather than good and today we played the good role but not the lucky one. If there is any criticism you need to hit the back of the net from the chances we had but (Tottenham goalkeeper) Hugo Lloris was outstanding with two saves," added Martinez.
"Spurs produced very little, just one shot on target and they win the game. It is one of those rare occasions."
While Spurs fans applauded Adebayor they also gave Jermain Defoe a rousing send-off at the end after he was lifted on to the shoulders of his team mates and did a lap of honour.
The London club's fifth highest scorer of all time is leaving at the end of the month for Major League Soccer team Toronto and his five-minute substitute appearance will be his last at home in the league before he goes.
"He's been a legend at this club and he deserves 10 standing ovations but we've got other games to play before he goes. He's far from finished unless he hasn't told me," Sherwood joked.
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