Jurgen Klopp's side netted two late goals, including a stoppage-time header from Sadio Mane to walk away with all three points, as Liverpool had 74% possession on the day, according to BBC Sport.
Despite being so dominant with the ball, Villa would argue that they were the better team in the first half, but after the break, the Reds started to push the home team further back, as the majority of their 25 shots on goal came after the break.
Speaking to BBC Radio WM, Smith shared that he told his Villa players that they were 'outstanding' on the day, as he also expressed his views on Liverpool's possession.
"It certainly is [a bitter pill to swallow]," Smith told BBC Radio WM. "I just said to the lads that I am proud of them, I thought they were outstanding, especially in the first against a top team in Europe.
"They'll argue that they have had lots of possession, and they have, but Tom Heaton hasn't been making a lot of saves. They had a chance when Lallana should probably score, they had the VAR goal overturned when the flag goes up early and that's there. But we have had them disallowed. For offsides, they are factual, so we know where the line is and where the bar is."
In the first half, Heaton didn't have much to do, but Liverpool will feel hard done by because Roberto Firmino's goal was wrongly ruled offside by VAR.
After the break, the relentless pressure continued from the away side as Adam Lallana scuffed his effort well wide, Heaton saved a header from close range before he saved Trent Alexander Arnold's free-kick, which ended up leading to a corner, which led to the goal.
In the end, Liverpool walked away with the points, as they are still six points clear of second-placed Manchester City, who had to come from one goal down from their own game against Southampton.
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