Villa stretched their unbeaten run to six league games after a highly entertaining clash at Craven Cottage in which the home side missed a penalty and both teams had a player sent off.
Fulham were in front after five minutes through Raul Jimenez, but Morgan Rogers put Villa on level terms just four minutes later before Ollie Watkins and an own-goal by centre-back Issa Diop sealed all three points for the visitors.
The win took Villa to fourth place in the standings with 17 points from eight matches, just one shy of leaders Liverpool, who have a game in hand.
"Every match we play is a difficult match and we have to be very, very consistent, focussing each moment being 100%," Emery told reporters.
"I am very happy because we reacted very well, playing being serious and mature.
"We have to be consistent like last year. Our objective is through the Premier League and we are building again with some new players and some players they are coming back from long injuries.
"New players as well are progressively adapting better... We have to prepare the team for lots of matches."
The West Midlands side secured a spot in Europe's top-tier club football competition for the first time since 1983 after a fourth-place Premier League last season.
Villa won the old European Cup, precursor to the Champions League, in 1982, but had not played in the continental competition for 41 years.
They are targeting more success this campaign.
"We were very focussed in our demands to get Europe and achieving Champions League and we are enjoying it, but today the Premier League was most important for us," the Spaniard added.
"The supporters are aware of how important the Premier League is for us to play again in Europe next year, hopefully in the Champions League."
They next host Italian side Bologna in the Champions League on Tuesday.