Los Che thrashed AZ Alkmaar 4-0 at the Mestalla last night [Thursday] to overturn a 2-1 first-leg deficit, while Atletico saw off Hannover 4-2 on aggregate to set up an all-Spanish last-four encounter.
Emery said: "The tie against Atletico will be very demanding. We did not want to face Atletico, and they did not want us, but the fact is that this tie has beautiful connotations."
The tie will be a repeat of the Europa League quarter-final two years ago, which saw Atletico advance on away goals after Valencia were denied a late penalty for an apparent foul on Nikola Zigic by Juanito.
The team then coached by Quique Sanchez Flores went on to win the tournament.
Emery said: "When I saw who won that title... the truth is, I thought it could have been our time after a penalty not given to Zigic in the closing minutes of the second leg of quarter-final. But we now have the opportunity to be close to the title again."
Two goals in as many first-half minutes from Adil Rami sent Valencia on their way last night [Thursday]. The Spanish side were on top form with Jordi Alba and Pablo Hernandez also on target to wrap up a 5-2 aggregate success.
"It was a complete, consistent performance, with wisdom in the penalty area that sometimes we have not had," Emery said.
"We had an efficiency in our actions, and that gave us the victory. In defence we stopped the opposition better than the first leg, and that security helped turn the defence into attack. We were comfortable at the Mestalla."
With Athletic Bilbao also advancing to the last four, courtesy of a 6-4 aggregate win over Schalke, and Barcelona and Real Madrid into the Champions League semi-finals, Emery hailed the state of Spanish football.
He said: "We are pleased and excited at the ability of the Spanish teams. To have got five semi-finalists in European competition, as well as the success of the national team... It is a positive time to talk about Spanish football."
Having won only once in La Liga 2012, though, Emery's side have let slip their hold on third place in the standings and the coach has promised the team will give everything on all fronts in the run-in.
"The team is suffering in the league, and we must stop this situation," he said. "We will fight in all competitions for the remainder of the season."