The Reds looked set to claim three points from Manchester City on Sunday after twice taking the lead, first through Martin Skrtel and then with a memorable free-kick from Luis Suarez.
However, a late pounce by Carlos Tevez levelled the game at 2-2.
Enrique, though, thinks there were a lot of positives.
"I think we did really well and we deserved to win," said the Spaniard, who returned from injury as a substitute in the second half.
"We made two mistakes and they punished us with two goals. But to get a point against Manchester City is not a bad result. This team was the best team in the league last year and today we were better than them.
"We are still learning with a new manager and some new players and of course we need some time but if we keep playing like that then we will win many points.
"The manager wants us to try to keep the ball when we have it and then press hard like lions when we don't have it.
"We did that really high up the pitch against City. They had to pass back to their 'keeper many times or kick the ball long because we were pressing them.
"It's like tiki-taka. The best team in the world is the best example and that's Barcelona. We see how amazing they are with the ball and how when they lose it they win it back within a few seconds.
"We can't compare ourselves to them but we are trying to play like this."
Tevez's strike followed a misplaced pass from the otherwise outstanding Skrtel.
"Martin feels bad — like anyone would when you make an error like that. But Martin is one of the best centre-backs in the country," Enrique told the Liverpool Echo.
"Anyone can make a mistake. We have already forgotten about that and are focusing on the next game. It's in the past and now we have to think about the big games in the future.
"We have Hearts on Thursday and then Arsenal next Sunday. We have to keep playing like this."
Meanwhile, the game was marked by a first Barclays Premier League start for 17-year-old Raheem Sterling, who showed poise and imagination on the ball as well as a willingness to fulfil his defensive duties.
"Raheem has done really well in the last two games he has played for us," said Enrique.
"He worked really hard and his positional play was good. Everyone knows the qualities he has — he's an amazing youngster.
"He's quick and he has everything, but we have to be quiet about him.
"He's still young — only 17-years-old — and still has a lot of things to learn. But if he continues like this and continues to listen to the manager then he will be a great player for us."
Photo via Facebook/Hillsborough 1989 – Don't Ever Forget