Speed, 42, was found hanged at his home after apparently committing suicide.
Earlier, Welsh side Swansea City drew 0-0 with Aston Villa with fans bursting into spontaneous applause during a minute's silence in his honour.
The first goal of the day came at Anfield where City, who finished the match with 10 men after substitute Mario Balotelli was sent off, took the lead in the 31st minute with a Vincent Kompany header.
Liverpool equalised two minutes later when Joleon Lescott deflected a Charlie Adam shot past goalkeeper Joe Hart.
The England keeper had an outstanding match for City and made some superb saves to keep them in the game especially when they were down to 10 men.
Balotelli, who came on in the 65th minute for Samir Nasri, was booked twice in his brief appearance, first for pulling back Glen Johnson, then for appearing to lead with his elbow when he challenged Martin Skrtel for a high ball seven minutes from time.
Liverpool manager Kenny Dalglish withdrew Craig Bellamy from his squad, explaining the Welsh forward was too grief-stricken after learning of Speed's death.
"It was best for me to make the decision for Craig," Dalglish told Sky Sports. "He was very close to Gary who was almost a mentor to him, someone he admired and looked up to, and he was upset.
"There's no way a game of football is more important than grief."
Speed was the first player to chalk up 500 Premier League appearances as his career took in spells at Leeds United, Everton, Newcastle United, Bolton Wanderers and Sheffield United. He became Wales manager last December.
Dalglish was pleased his side became only the second this season to take league points off City who remain unbeaten having won 11 and drawn two of their 13 games.
City, on 35 points, stayed five clear of Manchester United, with Tottenham Hotspur third on 28. Liverpool moved up to sixth on 23 points.
"I think they started better than us but we were the better team at the end," said Dalglish.
"It was fortunate for us we got the equaliser as quickly as we did, it kept the spirits up. We tried our very best to win it in the second half but unfortunately we just could not get it over the line."
MANCINI BIRTHDAY
City, who had won their last seven league games but went to Anfield after losing 2-1 to Napoli in the Champions League in midweek, started the better team but were left hanging on to a point at the end.
Manager Roberto Mancini was satisfied with a draw on his 47th birthday but added Balotelli should not have been sent off.
"It's a good result for us because we played with 10 men for the last few minutes," the Italian said. "But for me the second Balotelli foul was not a yellow card, he didn't deserve it."
Earlier, Swansea's match with Villa was played in a subdued atmosphere at the Liberty Sta
