Puel saw his side squander a number of good openings, while opponents Liverpool struggled to truly get going all night, yet the Frenchman knows that more is now required to get over the line on Merseyside in two weeks' time.
Speaking to Sky Sports News after the match, he said: "We are deserving this result with all the many chances we had. It was important to win with the clean sheet and we can have a strong game at Liverpool. I think Liverpool had just the one chance all game. We were unlucky at the end because we know Liverpool away in the second leg will be very difficult.
"It was the same in the Premier League - a strong defence - but this game was interesting because we were strong in defence and were better to keep the ball and to have a very good counter attack. It was a very, very good game but it is just the first leg and we are just one goal up.
"This competition is exciting, now it is important to keep the good concentration for the Premier League. We lost three games so it is important to have the good reaction."
Southampton's league campaign resumes at Burnley on Saturday afternoon, before the visit of Leicester City eight days later.