The Uruguay star struck in the 90th minute to cancel out Alex Alegria's opener and salvage a point from a match in which the champions had largely been second best.
Jordi Alba thought he had levelled moments after Betis broke the deadlock in the 75th minute, the full-back bundling Aleix Vidal's cross well over the line before Aissa Mandi hooked it clear, but referee Alejandro Jose Hernandez Hernandez failed to award the goal.
Another deflected Vidal cross almost went in just a minute later, although Mandi this time cleared before the ball had gone in, but Betis' efforts proved in vain as Suarez turned in Lionel Messi's pass to equalise.
Speaking afterwards, the striker admitted it was frustrating not to be awarded the goal but urged his team-mates to look for ways to improve after the result handed another boost to Real Madrid in the title race.
"The first one, the ball was a metre behind [the line], but the officials can also make mistakes," he said. "The pictures confirmed it was a goal.
"It hurts us because the objective is to win and we have to do that to keep the pressure on those at the top.
"We did a lot to deserve the win earlier. That's football, because they also had a chance to kill it at 1-0.
"We showed that we want to stay at the top but we couldn't do it. We don't have to give them credit, we have to be self-critical.
"We had to win and now we depend on the rest losing. We knew it was going to be very difficult."
Madrid will move four points clear - still with a game in hand - if they defeat Real Sociedad at the Santiago Bernabeu later on Sunday.