Werner opened the scoring at Stamford Bridge as Chelsea were taken to penalties.
While a calf issue prevented the German from stepping up to be one of the nominated five from 12 yards, Reece James slotted home from the spot to seal a 4-3 victory after the game had finished 1-1.
Chelsea will host Southampton in the fourth round.
“It’s good to be back on the score sheet, good to score at Stamford Bridge and I’m happy that I’m back on the pitch,” Werner told the club’s website after his side’s win.
“I think that the last few weeks were not very easy for me, but every goal, every assist brings me back on track, so it was good for me today and also for the team.
“I think both teams gave everything. Aston Villa were a very tough opponent and they showed why they are always very hard to play against. I think in the second half we were lucky to score an early goal, it gave us a little bit of a push, but 10 or 15 minutes after the goal we lost a bit of control when we conceded.
“After that we wanted to finish the game in 90 minutes, it was important. In the end it didn’t happen, but good penalties at the end saved us.”
Werner was full of praise for Kepa Arrizabalaga, whose save from Marvellous Nakamba proved the key after both Ashley Young and Ben Chilwell stuck the bar.
Kepa could again be forced to deputise for Edouard Mendy against Manchester City with the first-choice goalkeeper facing a “race against pain and time” to be fit after suffering a knock in last week’s Champions League opener against Zenit St. Petersburg.
Werner would have no concerns if Chelsea have to pick the Spaniard, who helped his side to UEFA Super Cup victory before the start of the new season with two shootout saves against Villarreal.
“Kepa is unbelievable in penalty shoot-outs,” Werner continued.
“This season already he has saved us two opportunities to win titles. He’s a great guy and a great goalkeeper.”