Spurs were awarded their second spot-kick of the match in the 93rd minute when Virgil van Dijk was adjudged to have fouled Erik Lamela just moments after Mohamed Salah had put the hosts ahead in stunning fashion.
Having seen his first penalty of the game stopped by Loris Karius, Harry Kane coolly finished his second to earn a share of the spoils for the visitors.
And Alexander-Arnold could not hide his disappointment as he spoke to Liverpoolfc.com shortly after the full-time whistle.
"It's very bitter to come out with only one point at the end of the day because we held on for the majority of the game," the defender said.
"Loris did well with the first [penalty] and then the second one, it's hard enough to save one pen, so there was no pressure on him to try and save the second.
"They got that late goal and it was devastating."
Mauricio Pochettino's team were the dominant force in the second half, controlling possession and exerting pressure on the Reds' backline throughout.
But Alexander-Arnold was pleased with the manner in which the hosts stood up to that test.
"They're a top, top quality side and there were always going to be spells where they dominated possession and created chances against us. We had to be ready for that and we were, to an extent," the Academy graduate added.
"They scored a long-range goal and a penalty and it was one of [those] - two goals that happen on rare occasions.
"We've come away really disappointed because we played quite well for the majority of the game."
The No.66 now wants Liverpool to move on quickly from any feelings of disappointment and refocus ahead of Sunday's trip to Southampton.
"It's past us and we have to look forward to the next game and get the three points next week," he continued.
"[We can't] dwell on it too much because we have to go back out there and get the three points against Southampton. We've still got a lot of games to go in the rest of the season and each week there are three points on the line.
"Unfortunately today we could only get the one point but it's better than getting nothing at the end of the day."