The Manchester United loanee has warned his side not to get complacent following their 1-0 win at Tottenham Hotspur.
Christian Benteke’s first-half header at White Hart Lane saw Villa go six points clear of the relegation zone with five Premier League matches remaining, as Tim Sherwood’s side leapfrog both Hull and Sunderland into 15th-place in the table.
The result also puts the club just one point behind Midlands rivals West Bromwich Albion, who have now been dragged back into the relegation scrap following three consecutive defeats.
The on-loan Manchester United midfielder was quick to praise his team’s performance at the final whistle, lauding manager Shewood’s gameplan, but highlighted the Baggies’ current plight to underline how survival is far from assured at this point in time.
Asked whether Villa were safe now, he said: "Definitely not. Just look at West Brom. They looked safe a couple of weeks ago and they've been dragged right back in.
"We won't be taking our foot off the gas."
Continuing on the manner of the win, Cleverley added: "We have come here and produced a very mature and professional performance. And I think we deserved the three points.
"Playing the diamond formation, it gave our full-backs plenty of room and when we switched the play we caused them problems. We hit them on the break too.
"The goal came from switching the player to our full-back and the big man finished brilliantly. He's on fire. Full credit to him.”
Villa now take a brief break from the Premier League survival race to take on Liverpool in next weekend’s FA Cup semi-final, before their final five top-flight fixtures pit them against Manchester City, Everton, West Ham United, Southampton and Burnley.