Barely four months after sweeping Juventus aside 3-1 to win the final in Berlin, Barcelona set their sights on beating another Serie A side into submission as they look to become the first side since AC Milan in 1990 to win back-to-back European titles.
But despite a dominant performance throughout, the Catalans were left frustrated as Bayer Leverkusen, 4-1 winners over BATE Borisov, went two points clear at the top of the group.
In what was Lionel Messi's 100th Champions League appearance, the Argentine was upstaged by Alessandro Florenzi's stunning leveller for the hosts from just inside the halfway line on 31 minutes.
Enrique, who spent a fruitless season as coach of Roma in the 2011-2012 season, said: "I would have expected us to come up against a more attacking team. Instead, they chose a different approach.
He added: "I'm satisfied with how we played, we created a lot of chances and when your opponents close up at the back it's not easy."
Barcelona striker Luis Suarez said: "We know Italian teams. They close up at the back and it becomes very difficult to find space to score goals.
"We controlled the game in possession and created a lot of chances. They managed to score from distance, but they were lucky there too."
Given Barcelona's firepower, and the fact Roma were humiliated by a 7-1 thrashing at the hands of Bayern Munich in January, the Giallorossi had every reason to go on the defensive.
Despite a series of counter-attacks by Egyptian winger Mohamed Salah offering promise early on, Barcelona gradually settled into their trademark possession and passing game to leave the Stadio Olimpico eerily silent as fans watched in awe.
A day after seeing Real Madrid striker Cristiano Ronaldo overtake their shared record of 77 goals in the competition with a hat-trick in a 4-0 win over Shakhtar Donetsk, Messi was on the hunt for goals.
But despite dipping and skipping his way past opponents to set up chance after chance, Roma's defence - and a superb display by the hosts' goalkeeper Wojciech Szczesny before he suffered an injury early in the second half - Messi was not to be satisfied.
Messi's most telling contribution came on 21 minutes, when he backed into Lucas Digne, causing the Frenchman to fall.
The subsequent confusion over whether a foul had been committed gave Barcelona a split second's momentum and Rakitic went unchallenged at the near post to send in a lob for Luis Suarez to head home at the back post, as Roma's players protested in vain.
Roma coach Rudi Garcia's diplomacy did not allow him to point the finger, but the Frenchman managed to get the point across afterwards.
"Florenzi's goal, which was legendary, obviously cancelled out their opener. But before they scored he had been taken out of the play and couldn't defend," said Garcia.
Almost immediately afterwards, Barcelona were denied a possible penalty when Szczesny missed the ball when at full stretch to deny Suarez at the Uruguayan's feet.
Fans were expecting the worst, until the stupor was broken in spectacular fashion just after the half hour.
Seeing goalkeeper Marc-Andre Ter Stegen 15 yards off his line, Florenzi carried the ball into Barcelona's half near the right touchline, looked up and hit a drive that sailed over the keeper, off the far post and into the net.
"I couldn't believe it went in," said Florenzi, who none the less has a habit of scoring the occasional spectacular goal in Serie A.
"I held up my hands to my face in disbelief. I don't do that very often."
"That was one for the history books," said Garcia, whose side next face BATE Borisov in a fortnight.
"Against Barca you always concede chances but the boys did well to close a lot of those down," he added.
"It's not a great result, it's a good result that has given the lads some confidence for our subsequent matches."