The boss takes his Barclays Premier League team to Sunderland on Saturday for a crunch clash.
The Black Cats are a point and a place ahead of fourth-bottom Villa, who themselves are just three points above the drop zone.
And with the Cheltenham Gold Cup on Friday, Sherwood is hoping Villa, who have never been relegated from the Premier League, can avoid being unseated.
He said: “I think it’ll be a photo finish and I hope we’re not in it.
“We’re probably just coming around the corner but it’s probably the longest run-in in racing history.
“All we’re looking at is the next fence and that’s Sunderland. After that we hope we can stay in the running. There might be a few who fall along the way and we’re hoping that’s not us.”
Villa have won their last two under Sherwood, beating West Brom twice in the league and the FA Cup to reach the semi-finals.
They were the new manager’s first wins since replacing Paul Lambert in February and Sherwood has been impressed with the squad’s attitude.
“They’ve been good and a win makes an awful lot of difference. They have been focused and up for the fight,” he said.
“They haven’t dwelt on the position. It’s about looking forward now, what we have done previously counts for nothing.”
Sherwood, before becoming head coach, was at Tottenham as assistant first-team coach under Harry Redknapp and worked with Sunderland striker Jermain Defoe at White Hart Lane.
The 32-year-old returned to England in January after a year with Toronto in Major League Soccer and Sherwood believes Defoe is the Black Cats’ chief threat.
He said: “If they are going to survive it’s going to be Jermain Defoe who keeps them in the Premier League, that’s why they forked out that sort of money for him.
“He didn’t have to go, he went for a lifestyle change to Canada but he still has that appetite to come back and play for Sunderland, in a relegation battle.
“Jermain can score goals on his own but he prefers people to slide the ball across the six-yard box for him to be in the right place at the right time, that’s what he’s done all of his career.”