Sunday's 2-0 win over Crystal Palace breathed fresh life into Villa's survival bid and left them four points from safety ahead of Thursday's trip to Everton.
It was their first win since January and came after Watford and West Ham had won to initially leave Villa seven points from 17th spot.
The Hornets and the Hammers meet on Friday and head coach Smith is eager to see his side take advantage and close the gap.
He said: "I'm feeling the same as before the Crystal Palace game because not a lot has changed. We needed to win because the teams around us had won their games.
"We managed to get that win and it will give everybody a lift, but we're still in the same position. We can go and get some scoreboard pressure on Watford and West Ham who play the following evening.
"We've got to make sure we concentrate on our own game and put in a good performance. We certainly won't get complacent after one win."
Smith is likely to be without Kortney Hause (rib) and Neil Taylor (hamstring), while Danny Drinkwater is out having not trained this week following a knock.
Everton were outclassed by Wolves in their 3-0 defeat at Molineux on Sunday, leading boss Carlo Ancelotti to criticise their attitude.
And Smith is expecting a reaction from the Toffees at Goodison Park.
"They've got a manager who won't be accepting after the Wolves performance and result and they'll come out fighting.
"It looks like they've got some of their injured players back with Mason Holgate and Andre Gomes, who cost more than our record signing. That just shows that they are a very well-established team."