Sherwood had admitted in the build-up to the game that uncertainty around his future made him feel like a "supply teacher" amid claims from midfielder Sandro that the coach would be disposed of in the close-season.
The 45-year-old also revealed that some of his players have been informed by their agents that a new coach will be at the helm next season.
Despite the speculation, Spurs cruised to victory at White Hart Lane and clinched UEFA Europa League qualification ahead of Manchester United, with Paulinho capping off an intricate move for their first after 14 minutes.
The hosts had to wait another 21 minutes for their second as Nathan Baker scored an own goal, but it was no less than Spurs deserved against an unimpressive Villa side.
Emmanuel Adebayor grabbed the third from the penalty spot towards the end of the first period and although Villa were slightly improved after the break, Paul Lambert's men rarely showed anything to worry the hosts.
One of most positive aspects of Sherwood's reign has been the resurgence of Adebayor and the forward set up Harry Kane twice in the opening 10 minutes, but both times Brad Guzan denied the England Under-21 international.
The American's efforts went unrewarded in the 14th minute, however as Gylfi Sigurdsson's pass was flicked into the path of Paulinho by Kane and the Brazilian slotted home at the second attempt.
Despite falling behind, Villa showed no appetite to draw level and found themselves 2-0 down in the 35th minute as Baker knocked Danny Rose's drilled cross past his own goalkeeper.
Three minutes later, Gabriel Agbonlahor made his side's position even worse as he blatantly blocked a shot inside the area with his elbow and Adebayor smashed in the resulting penalty.
With victory effectively secured by half-time, Spurs appeared rather more relaxed in the second half and Fabian Delph almost pulled one back in the 57th minute, but he fired agonisingly wide from range.
Villa continued to see more of the ball than before the break, but still they struggled to craft many chances of note as Spurs remained solid at the back.
Sherwood's reportedly fractious relationship with Sandro has lingered throughout his time in charge, but neither showed any sign of ill-feeling toward the other as the Brazilian was replaced just after the hour mark.
Villa recorded their first shot on target in the 82nd minute as Delph tried his luck from distance but Hugo Lloris easily collected and Spurs claimed the three points to secure sixth, while their visitors end the season 15th.
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