The Gunners thought they had secured a crucial win when Robin van Persie scored a 98th minute penalty, but Dirk Kuyt equalised four minutes later with a penalty of his own.
The result leaves the Gunners' title aspirations hanging by a thread as they sit six points behind leaders Manchester United with six games to play.
Arsenal have now drawn their last three home games – against Sunderland, Blackburn and Liverpool.
Wenger says 'the hope is there' and his side must beat Tottenham on Wednesday night, but the Frenchman concedes his side are swimming against the tide.
“We will have to give everything until the last game of the season,” he said. “I don't know if it's our year or not. We have been badly done in our last three home games. It's a period when we have not had the biggest luck, that's for sure.
“We have to win the next game now. The hope is always there but to keep the hope alive we have to win our games. We are on a 15-game unbeaten run but recently have not taken enough points.”
Wenger appeared to clash on the touchline with Liverpool boss Kenny Dalglish after the Reds were awarded a penalty for Emmanuel Eboue's clumsy challenge on Lucas Leiva.
The Gunners boss was furious with referee Andre Marriner's decision to award the spot-kick but would not elaborate on his heated exchange with Dalglish.
“I told him [Dalglish] it was not a penalty,” Wenger explained. You can check what I said – it must be on television.
“It wasn't a penalty. Lucas stood in his way and stopped his run to got to the ball. It's not a penalty.
“We conceded the penalty after 11 minutes and injury time was eight minutes. I don't see where the extra three minutes time came from and I don't think it was a penalty.”
The 61-year-old also claimed Liverpool arrived at the Emirates 'only to defend' but accepted his side looked jaded and struggled to create chances.
He added: “It was difficult for us to create chances because they defended very well. We tried – we gave absolutely everything to create chances.
“Most Premier League teams come here only to defend. We had the ball and they always had eight to 10 men in their half.
“At the moment, we have problems creating chances. Some of the players are jaded, they have played 40 to 45 games and lack a bit of pace.”