The Hungarian midfielder had looked set to be Liverpool's match-winner at Anfield after firing the home side ahead in the first half. Szoboszlai converted a well-placed free-kick to give the Reds control of the contest and reward a dominant opening period.
Liverpool appeared comfortable for long stretches of the match, restricting Tottenham to very few clear opportunities. But the visitors struck at the last possible moment when Richarlison reacted quickest in the penalty area to score from close range in the final minute of normal time.
Speaking after the match, Szoboszlai did not hide his frustration.
"Yeah, it is a huge disappointment," he told Sky Sports. "I don't know what happened with the performance, to be honest. Really nothing to say."
The midfielder admitted Liverpool were again punished late in a match, something that has troubled the side several times this season.
"Again in the last minute. I don't know how many times it happened already this season," he said. "Really, I don't know what to say. We have to wake up."
Szoboszlai felt Liverpool had full control in the opening half.
"I think in the first half we played very well. We controlled the whole game. I guess they hardly created any chance, maybe one or two headers," he explained.
"But the second half it seems we go out and we don't do the same things like in the first half. The question is why? We will probably sit down together and talk about it. This is a difficult time, but we have to stick together."
The draw left Liverpool fifth in the league table, two points outside the top four places that guarantee qualification for the UEFA Champions League next season.
Despite the setback, Szoboszlai insisted the squad must remain united.
"There is still time to show how much we want it," he said. "We have to fight for each other and fight for the club because everybody wants to play Champions League next season."
Liverpool now turn their attention to a European clash with Galatasaray at Anfield on Wednesday before travelling to face Brighton at the American Express Stadium in the Premier League on Saturday, 21 March.
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Mikel Arteta has called on his Arsenal players to deliver a "complete performance" as they prepare to face Bayer Leverkusen in a decisive Champions League clash at the Emirates on Tuesday night.
Chelsea have been handed the largest fine in Premier League history and a suspended transfer ban after admitting to historical financial rule breaches involving more than 47 million pounds in undisclosed payments during the Roman Abramovich era.
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