The south coast side, who are 13th in the league table, travel to face Watford on Saturday.
"For now it is important to keep our concentration about the Premier League. It is a strong challenge ahead," Puel told the club's website.
"The journey in this competition (League Cup) was amazing, with young players at the beginning of the competition and after that experienced players.
"We produced a great final. It was a good competition but, of course, the most important thing was to win it, and this result is difficult for us."
After the clash at Vicarage Road, Southampton are not in action again until they travel to Tottenham Hotspur on March 18.
"We will stay two weeks with just one game, and this is difficult for the concentration and motivation. It is important to rise to this difficult challenge," Puel added.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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