Gerrard's header cancelled out John Terry's opener, but Liverpool could not find the winner they needed to keep the pressure on in the race for Champions League football.
Gerrard, who will leave Liverpool at the end of the season for the Los Angeles Galaxy, was substituted with 10 minutes left, and left the field to a standing ovation from the fans he came so close to joining in Mourinho's first spell at the Bridge.
The former England captain was on the end of lavish praise from Mourinho earlier this week, and he admitted: "I have huge respect for him. He's the best manager in the world for me and I'd have signed for him a couple of times if I wasn't a Liverpool fan.
"He's the reason why my head was turned on a couple of occasions but he understood why I couldn't do it."
However, Gerrard admitted the point would not be enough for his side in the race for Champions League football.
"Even if we'd won today maybe it wasn't enough, I still fancy United to take some points from their last couple of games," he told Sky Sports 1.
"This team has to build for next year and we wanted to make a statement and show that with additions and a bit of improvement we can compete next year."
He added: "I think it's important the players get some rest and the owners dig deep to try and help Brendan and the lads out and try and make some additions and improve.
"There's a great core of players here, some great potential but it's important that you try and compete with the giant clubs in the league because they're going to spend big every single year and it's important to keep up."
Mourinho was happy with the point, after admitting clinching the title last week played a part in a subdued performance. He said: "(It) was a good performance if you understand the circumstances.
"The team that is champions in the last weekend, it is normal that you lose your intensity of your mental approach but we worked hard to have players at a positive level and we were competing for a result."
On Gerrard, he added: "I will miss him yes, I want my league to be always the best league and have the best players.
"I have seen the end of amazing players and I was always hurt by that. Steven is leaving, Frank Lampard is leaving, Carragher, also a fantastic enemy also left last season."