The visitors went ahead after Martin Skrtel fouled Victor Moses with a clumsy challenge and Shaun Maloney slotted the subsequent penalty past a helpless Pepe Reina.
Luis Suarez equalised with a slick finish after the break, but a miraculous turn of events saw defender Gary Caldwell grab the winner with a striker’s finish just a few yards from goal.
Martinez told reporters: “It’s an historic day for us, beating Liverpool at Anfield, that’s why we’re involved in football and I would like to present this moment to our fans.
“They’ve had not much to celebrate this season and in the manner that they supported us against West Brom in one of the most dominant performances I’ve seen in the Premier League and we got just one point. I think today is a day we can be very, very proud.”
Martinez admitted he was surprised as anyone to see Caldwell grab the winner in the fashion the defender did.
The Spaniard continued: “I think he surprised the whole Anfield crowd and he surprised our own bench, it’s not too often you see Gary in those positions, but the composure that he showed is a fitting momentum, he’s a leader, he’s a captain, a rare breed.
“They are a dying breed, he’s been through difficult moments with us [but] always showing the right attitude, pushing the team ahead and I think he deserves to have his name for the winning goal in this historic moment for us.”
On his team’s performance, Martinez praised the cool heads of his players to keep the game calm and in their favour.
He added: “Liverpool started with an attacking momentum, they threw everything at us and we let ourselves down in those situations, we gave the ball cheaply in the wrong areas, we get heavily punished and then how many times have you seen the home side take control and then it’s just a routine victory.
“What I’m proud of is the players knew how to keep the situation, I thought we kept the ball really, really well, we took the sting out of the game in a very mature fashion.
“I don’t think many could argue that we didn’t deserve the win, just for the manner we stopped Liverpool, I don’t think they looked fluent at all and that’s down to the hard work that players put in.
“I think anyone in the bottom three is capable of getting points against anyone and we’ve seen that in the week. It’s [winning] a real way to shape up all those aspects that you cannot control on the training ground which is the belief, the confidence, the feel-good factor that you get from a win at Anfield.”