The Wales midfielder, making his Anfield debut, impressed as Brendan Rodgers' side twice took the lead against City.
Crucially, though, they twice lost it, with Yaya Toure and Carlos Tevez responding to goals from Martin Skrtel and Luis Suarez.
"It was pretty frantic. It was a brilliant game for the neutral and it was great to go ahead twice, so we're disappointed not to win the game," he told Sky Sports 1.
"Bittersweet probably sums it up perfectly."
Sunday's draw came eight days after the Reds' opening-day humbling at West Brom.
Anticipation was naturally high at that point, with Rodgers in the dugout for the first time, but Liverpool were crushed 3-0.
"We knew we would bounce back," Allen added. "We put that behind us and we will look to kick on from here."
There was a clash of styles on show today, with City's three-at-the-back powerhouse approach going up against a new, slick-looking Liverpool.
"Playing three at the back is not something many teams do," Allen said.