The loss followed their impressive 4-0 win over Fulham at the weekend and left Liverpool in 10th, eight points behind fourth-placed Tottenham Hotspur.
Spain's Enrique, who joined from Newcastle United in 2011, said he thought Liverpool would win when they took the lead through a Steven Gerrard penalty after two minutes but the visitors' advantage lasted just three minutes.
"We have to get a winning mentality going and we have to show what we are all about," Enrique said on the club's website.
"We need more experience and need to show more character in these type of games. You can see we have quality players and we have a good squad, but we need to fight for every point we play for if we want to be in the top four."
Stoke used their physical superiority to score twice through Jonathan Walters, who levelled the game after five minutes and registered his second early in the second half, while strike partner Kenwyne Jones was also on target.
Liverpool manager Brendan Rodgers bemoaned bad luck for Walters' first goal but said his team simply had to be better to keep out the opposition if they were to be more consistent.
"We were terrific at the weekend but you have got to be able to put a run of games together. That's been the nature of the group over the last couple of years in terms of where we have finished," Rodgers said.
"We're looking to improve that. There is still an awful lot of work to do. I have no doubt about the characters we have - we have some big characters and big players, but it was just too easy for them."
Rodgers agreed with Enrique that the players needed to show more mettle when they came up against physically imposing teams such as Stoke.
"You have to earn the right to play in whatever game - and in particular when you come to here. You know you are going to get pressed," said Rodgers, in his first season as Liverpool boss.
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