Barca remain six points off leaders Real after Sergio Ramos' last-minute header made it 1-1 after Luis Suarez had opened the scoring.
"In the second half, we were the better side, but we didn't manage to get the second goal and they ended up equalising," said Enrique.
"That said, we deserved to win. It is not the best result for us."
Barca were poor in the first half but looked set to close the gap on unbeaten Real to three points before Ramos headed home Modric's free-kick.
"It was a very even first half and a second that we were better, we created chances. We continued looking for the second to avoid being levelled, but we were unable to do so," added Enrique.
"In my opinion, the performance of the team was higher than that of the rival, but we have to improve, it is clear.
"I say this even when we win, and even when we draw. We can improve in all aspects of the game. We are ambitious."
Enrique was happy to see captain Andres Iniesta return from an injury that has kept him out for six weeks.
He came on as a second-half substitute and set up a Lionel Messi chance, which the Argentine missed, with a brilliant through ball.
"It is clear that Iniesta is a unique player and his input was perfect," added Enrique.
"He entered at a key moment and, despite the difficulties of being out for so long, he gave us quality, vision and hard work."

Robert McNab was sentenced to almost three years in jail for downloading indecent images of children, sharing them and sending offensive messages.
The 30-year-old admitted carrying out the offences between 2007 and 2016 at his flat in Greenock.
He was also given a two-year licence, which means he will be monitored after being released from prison.
Greenock Sheriff Court heard how McNab, who has previous convictions for hoarding indecent images of children and sexually assaulting a young girl, chatted to people on Facebook and WhatsApp using a fake name.
He talked about sexually abusing children and raping a baby.
The sex offender, who is also known as Robert Aitman, was found to have a stash of indecent pictures and videos - including footage of babies and children up to the age of 14 being sexually abused.
Defence solicitor Gerry Keenan said McNab was the victim of repeated sexual abuse when he was a child.
"Clearly there are issues which would require to be addressed in the public interest to minimise and reduce the risk of further offending," he said.
He asked for McNab to be spared jail and said he would engage with a treatment programme for sex offenders.
However, Sheriff Derek Hamilton ruled that a custodial sentence was required for such a "disturbing" case and jailed him for 35 months
He was also placed on the Sex Offenders Register for life.
Barcelona boss Luis Enrique said they "paid the price" for missing chances in their dramatic draw with Real Madrid.
[NEXT_CONCEPT]
A man has been jailed after he told a stranger that he wanted her to have a baby with her so he could abuse it.