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.
"We had to make changes to deal with it and for the first 15 minutes we struggled to get to grips with them.
"We play three in the middle and we didn't chance too much.
"Personally for me it was fantastic to make my debut and it was a great occasion and atmosphere."
For City, it was a point saved, with Tevez's goal his 100th in the English game.
Manager Roberto Mancini was not as happy as he could have been, though, calling for an end to the defensive sloppiness that has blighted his side over recent times.
They have shipped two goals in each of their last four games and the Italian said: "This is the time to finish conceding two goals every game.
"But we have taken one point when we went down two times.
"We started with the ball for 30 minutes, we had it in their half and had four or five chances to score.
"But we conceded a goal from a corner and something changed."
Despite boasting an embarrassment of riches in his squad, Mancini is still keen to bolster it before Friday's deadline.
Swansea's Scott Sinclair has been heavily linked, and Mancini said: "We have five days and we should work really hard, but no-one spoke to me during the game about Scott Sinclair."
For his part, Rodgers hailed his players as "incredible". Renowned for favouring a passing style of play, Rodgers is overseeing the start of a new era at Anfield and was happy with how today panned out.
"My glass is very nearly full," he said.
"I thought it was a brilliant performance. We were asked a lot of questions and I thought the players were incredible. Some times the best team doesn't win.
"Let's remember we were playing a good side."
With his passing ethos in mind, Rodgers also cleared Skertl of blame after his backpass fell short to allow Tevez in for his goal.
"He was brave enough to play it and that's the development of the team. As a group we will only get better," Rodgers said.