The Hammers travelled to Yorkshire on a run of five straight defeats in the Premier League and with Moyes under major pressure.
The home side took the lead through Wilfried Gnonto midway through the first-half, but Lucas Paqueta’s penalty and Gianluca Scamacca’s strike either side of the break turned the game on its head.
However, the Irons were unable to hold on as Rodrigo Moreno’s 70th-minute strike saw the home side draw level, before both teams missed late opportunities for a winner.
“I thought it was a sort of good old fashioned game at times,” Moyes said. “I thought when we went 2-1 up we would go on and win the game and actually, if anything, we gave the game back to Leeds United. We shouldn’t have done it.
“It felt like a step in the right direction. Getting a point away from home at Leeds United is a good result for lots of teams and it is for us at the moment.
“I actually felt like we missed an opportunity to get all three, I really do.”
Moyes also paid tribute to West Ham co-chairman David Gold, who passed away earlier on Wednesday at the age of 86 following a short illness.
“David Gold was incredibly supportive to me personally,” he added. “He wanted me to stay after the first time and was thrilled when I came back the second time.
“He was regular visitor to the training ground at Rush Green when he came in and saw us for his dinner. He was an old man, but a good man and when he talked, he was a sensible man.
“It’s a big miss for us, but obviously his family is the biggest, they’ll be really disappointed to lose him but he hasn’t been well for a little while. Everybody’s really saddened by it.”