Liverpool moved up to eighth in the table with the win, just two points outside the top six, while the gap separating Villa from second-bottom Sunderland expanded to seven points.
"We knew about the importance of the game in our situation and in the situation of Aston Villa too, with the results and number of games (left). There are only 12 games left," Klopp told the club's website (www.liverpoolfc.com).
"We came out and... won 6-0. It (doesn't happen) too often in a manager's life, so we should keep it for bad times.
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"It was a good game for us, a result for the soul, for the table, for our goal difference, so everything was good."
Injury-prone striker Sturridge marked his first Premier League start under Klopp with the opening goal and the manager declared himself pleased with the England international's performance.
"We need the goals of Daniel and he needs the goals, that's clear," Klopp said.
"It's not a surprise that he can score goals of course but it's a surprise how well tuned he is with the team when he starts.
"With his movements, he's a real striker, that's good to see... but we can only speak about this when he's available. When he's not then we cannot say 'with Daniel it would have been different'."
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
