The Potters came from two goals down to go into the half-time break at 2-2 before the Reds restored their two-goal advantage prior to Jon Walters giving them some semblance of hope with an 85th-minute third.
But Daniel Sturridge saw off the challenge of Stoke with a late goal to wrap up proceedings in a game that Hughes felt got away from his players.
"Listen we have never been ahead in the game and unfortunately we had to force the issue and given the ability on the break they have got they got us a couple of times," he told Sky Sports.
"We just gave ourselves too much to do today.
"Unfortunately 2-0 down to a freak deflection (off Ryan Shawcross) and we didn't deal with a long punt up front (which Luis Suarez scored) so we are 2-0 down without them really having a shot on goal at that point.
"So we showed great character to come back level at half-time
"In terms of effort and determination to try and stay in game and affect the game I thought we were really good in that regard, but defensively we made too many errors today.
"I can't fault my players for effort and determination."
Stoke remained 12th on the table despite suffering a third defeat in their past four outings as the Reds stayed fourth after their 13th victory of the campaign.
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