Allardyce made his return to the dugout after heart surgery on Saturday.
“I felt okay until the last few minutes, they were a heart-stopper,” said Allardyce.
“But in those minutes we could have won it. Nikola Kalinic was through, and should have at least got his effort on target. He was flattened by (Jose) Reina just outside the box, but he still should have rolled the shot on target.
“I was delighted with the way the team played. It has been a good week for us, beating Chelsea in the Carling Cup as well.
“Considering our lads had played two hours and then penalties in that match, and Liverpool didn’t have a midweek game, I felt it was a great testimony to our fitness.
“We could easily have lost it in the second half, and I felt we deserved the bit of luck when (David) Ngog hit the bar.
“But there was also another chance we should have put away when Franco (Di Santo) was clear in the box. That is the difference between the big boys at the top and teams like us, they take those chances.
“But considering Liverpool are a great club, we restricted them to just that chance against the bar. As the game went on we put Keith Andrews on to man-mark Steven Gerrard, he was the best player out there.
“And that meant he could not get the space to produce a bit of magic to win it for them.”
