Pulis' side recovered from three goals down before the hour mark at Selhurst Park to equalise with two minutes of regular time remaining and the Welsh manager said Palace could have snatched all three points.
Liverpool, who moved a point clear at the top of the Premier League but having played a game more than second-placed Manchester City, looked set for a vital victory in London until Damien Delaney's goal and a brace from Dwight Gayle saw Palace steal a draw.
The result has all but ended Liverpool's title hopes, with City set to face Aston Villa and West Ham on Wednesday and Sunday respectively.
When asked if he believed Palace had opportunities to win the game at 3-3, Pulis said: "Yeah, 'Gayley's' (Gayle) effort right at the end and even Tom (Ince), when Tom broke down the left-hand side."
Pulis added that he always believed Liverpool's 'open' style would give his players chances to score.
"Came in at half-time (at 1-0 down) and I just said, we'll get through the first 10 minutes of the second half and I honestly think the game will open up, and if the game opens up and we get the opportunities and chances (to score), we'll have a chance," the 56-year-old said.
"They get two goals... and at 3-0 you're staring down the barrel.
"When we got the first goal, I actually thought we'd have a squeak and then the supporters, everything took off. It was amazing... and when the second goal went in, it was just a matter of time until we got the third."
But Pulis added that Palace's late comeback was just symptomatic of the 2013-14 Premier League season and predicted more twists before the campaign ends on Sunday.
"That's football. It's been the Premiership this year," he said.
"Don't write off Liverpool yet, that's the way the season's been."
The former Stoke manager, who took over at Selhurst Park in November with the club bottom of the Premier League, also hailed the performance of Gayle, who came off the bench in the 65th minute to score his fifth and sixth goals in all competitions this campaign.
"Gayley's been very unlucky this year," Pulis said.
"We've played a certain way and it's not really suited Gayley, but bringing (Glenn) Murray on with him - actually Murray took a lot of pressure off him - and he (Gayle) finds the gaps and the two goals were fabulous."
