The Goodison clash was tied at 2-2 until Suarez smashed home a Sebastian Coates knock-down in injury time.
The Uruguayan began to celebrate only to have his joy turn to despair at the sight of an offside flag.
Replays showed the goal was not offside.
"I've seen it again and we can feel sorry for ourselves because it was a clear goal," Gerrard told the Liverpool Echo.
"We should be taking away the three points rather than just one. There is no offside and it's difficult for me to explain it. The only person who can explain it is the linesman.
"I asked him after the game if it was offside and he said 'I think so'. That's not good enough. If every decision in this league is based on 'We think so' then we're in trouble.
"The linesman got it badly wrong. The benefit of the doubt is supposed to go to the attacking player anyway.
"And for their second goal, it's a clear throw-in to us. The linesman gives us the throw but the referee [Andre Marriner] saw something different. He gave Everton the throw and their second goal came from that.
"I feel sorry for our lads because I thought we were fantastic today and deserved to win.
"We had a young, small team out there but they were all men today and stuck together. There was one team here who came to play football and win the game and that was us."
The enthralling encounter was punctuated with controversy, including a dive by Phil Neville which earned him a yellow card.
Neville apologised afterwards but the incident left a bitter taste for Gerrard in light of pre-match comments from the Everton camp about Suarez.
"His manager did every paper, every radio station and every TV channel talking about Luis Suarez and then his captain, who is meant to be setting an example, blatantly dives.
"With what he said about Luis Suarez before, David Moyes was trying to get in the referee's head, which is fine, that's all part of the game, stuff like that, but you don't expect your captain to dive like that.
"Luis Suarez was fantastic for us again today. I can't control what he does when he scores a goal, I was just happy to see it hit the back of the net. He doesn't need David Moyes to fire him up. But if people want to try to get in Luis's head and wind him up then it's the wrong thing to do.
"You saw from today's evidence that it seems to inspire him rather than go against him."
Liverpool went 2-0 up early in the game before Everton seized the momentum to level ahead of the break.
Brendan Rodgers made two substitutions at the interval, reverting to three centre-backs and moving Raheem Sterling to a central position behind Suarez.
Gerrard was impressed.
"I think it was an off-the-cuff decision and credit to the manager for that," he said.
"That's one of the reasons why he got the Liverpool job. He's capable of making big decisions at big times.
"Everton were very direct in the first half and were getting on the second balls. The plan in the second half was to go 3-5-2 and try to stop the long balls coming in.
"Once we stopped that we passed through Everton and looked very dangerous on the break."