Villa became Spain's leading scorer when he netted his 45th and 46th goals for the world and European champions against Czech Republic last month, but last found the net for his club against Real Mallorca on February 26, a barren run of six games.
"You always get a bit worried when you aren't scoring but you have to stay calm," Villa told a news conference on Monday.
"I know it's been a while since I scored, but the only way to put that behind me is to work hard in training and on the pitch," the 29-year-old added.
Barca coach Pep Guardiola is likely to have fit-again forward Pedro and full-back Maxwell available for the clash at the Nou Camp as the Spanish champions eye a possible semi-final against great rivals Real Madrid.
The pair trained at the same pace as their team mates on Monday, Barca said on their website. However, captain and central defender Carles Puyol, who has a knee injury, is yet to rejoin the group.
World Player of the Year Lionel Messi, joint top scorer in this year's edition of Europe's elite club competition with eight goals, did not train as a precaution after an injury scare on duty with Argentina.
Barca are on a high after stretching their lead over Real at the top of La Liga to eight points at the weekend with eight games left.
DEFENSIVE WOES
Barca need to be careful of complacency after Saturday's 1-0 win at Villarreal and focus fully on the Shakhtar match, Villa said.
"When you come into a game after losing or drawing everyone knows you have to put it behind you and concentrate on the next match, but the same thing holds true if you've just won.
"Now we have to try and play well, win and get a good result for the second leg."
Shakhtar, who recorded a shock 3-2 win at the Nou Camp in December 2008 before Barca went on to win the final, have defensive problems.
Centre-back Dmytro Chygrynskiy, who had an unsuccessful spell at Barca last season, is struggling to recover from a minor injury picked up two weeks ago but could make the starting line-up.
His defensive partner Olexandr Kucher is definitely out and has travelled to Barcelona only for a consultation on his injured knee.
However, influential Brazilian midfielder Fernandinho is back in action after seven months out with a knee problem and played the whole of Shakhtar's 3-1 win away to FC Ilichivets Mariupol on Friday.
"Now I am ready to play all 90 minutes. In fact, the whole team are ready," Fernandinho said.
"It is the most important game for us because we have reached the quarter-finals for the first time," he added. "It would be perfect to score in Barcelona."
Shakhtar are in the last eight for the first time.
Probable teams:
Barcelona: 1-Victor Valdes; 2-Daniel Alves, 3-Gerard Pique, 16-Sergio Busquets, 21-Adriano Correia; 6-Xavi, 14-Javier Masc
