The Blues lead twice through a penalty on the half-hour from Dominic Calvert-Lewin and a goal early in the second half from the impressive Demerai Gray.
But Leeds, roared on by a raucous crowd of over 36,000 in the club's first game at Elland Road in front of a full house of supporters in 532 days, showed their character to level twice and avoid a second successive top-flight defeat at the start of a season for the first time since 1980-81.
Mateusz Klich scored their first equaliser five minutes before the break and a brilliant curler from Raphinha - who scored for the third successive game against the Blues - earned Leeds a point in thrilling fashion on 72 minutes.
Phillips, who returned to the starting line-up after being an unused substitute last weekend, commented: "It’s been amazing having the crowd back. The fans showed how much they’ve missed us and we've really missed them. Having a full crowd is like an extra man.
“We're disappointed not to take the three points, after a great finish from Raphinha. We all know what kind of player he is and to put it in the bottom corner first time like that was great
“It wasn’t the best of us today. It’s early in the season, and I feel like, especially me, could be a lot fitter and a lot stronger.
"Every team will create chances against us. We probably could have done better in the goals that they scored."
Offering his take, head coach Marcelo Bielsa said: "The game was a big test for the team. This was multiplied as we were behind twice. Given the amount of minutes we dominated, we should have created more chances on goal and we should have conceded less chances.
"We didn't start well in the second half and after the second goal, there were some concerning moments. But the effect to have gone behind once again is normal and because of that, we run the risk of conceding more goals."
Bielsa confirmed that Rodrigo started on the bench due to a slight muscle issue.
He commented: "It was just a muscular issue which has recovered quickly. He would have been our offensive midfielder, (if he was fully fit) but I have a lot of confidence in the quality of Rodrigo."