The Argentine manager however acknowledges that Sissoko's elbow was not where it was supposed to be - at Arter's face - which is why Spurs have accepted their third violent conduct charge in the past 13 Premier League games that includes last season.
However, the FA saw it differently and have confirmed that the 27-year-old has been charged and could face anything up to a three-game ban.
"After reviewing the video we have said that we accept the charge and now we move forward", Pochettino told reporters on Monday.
"He caught me straight in the face and if you get hit in the face anyone would have a reaction".
On whether Sissoko had apologised, he said: "I believe that it wasn't his intention what happened. It's clear. We accept the charge and now it's to move forward with him suspended for three games".
Arter initially reacted angrily to Sissoko's challenge as both sets of players clashed on the field, but later insisted he hoped the France midfielder would escape a ban. I'm not one to hold grudges.
"He said to me afterwards that he did catch me but that it was by accident".
The former Southampton boss insisted Sissoko had no need to apologise, however.
Sissoko is facing up to a three-game ban, although he had an unlikely ally in Arter after the game.
"It's always hard to play a big team like Liverpool".
"It's true that it's hard now, because he's a player that was in our plans to play tomorrow, and now we need to change a little bit".
The draw leaves Tottenham fifth in the Premier League with 19 points, just one point behind Manchester City at the top of the league.
"It's true that tomorrow we'll play Michel Vorm", said Pochettino.
In fact, the best chance of the match fell to the home side as Hugo Lloris was forced into an unbelievable save as he pushed a shot onto the bar from close range.