Southampton had taken the lead through Will Smallbone at Anfield but Liverpool responded with goals from Darwin Nunez and Mo Salah to win 3-1 in the second half.
Harwood-Bellis, 23, felt Saints "half deserved" to take the lead against the league leaders because they nullified their quality in the first half.
However, he admitted a "soft" Liverpool penalty, converted by Salah, "killed" Southampton's chances of earning a point on the road.
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The defeat leaves Saints 14 points adrift from safety at the bottom of the Premier League table following Wolves' 1-1 draw with Everton.
"It's not great to lose the game but I thought we fought well. In the first half, we were really good," the one-time England international explained.
"But we came out in the second half and, obviously the crowd (played a part) and the penalty kills us a little bit. I thought it was a bit soft, to be honest.
Southampton's Taylor Harwood-Bellis (right) tackles Liverpool's Andrew Robertson. _(Image: Peter Byrne/PA)_ "I thought we dug in and it was a better performance in terms of how we dug in. I can say we are proud of the boys for how we defended.
"It's the least we can ask for, but to do it against the best team in the league, I am proud of the boys."
He continued: "In a different way, I thought we half deserved to take the lead because of the way we nullified them.
"But we knew they were going to come out a different animal and they did. It's hard when the crowd is like that.
"We tried to slow it down but when they kill you, it's difficult. When they give a penalty like that, it kills us a little bit.
"There is stuff we can build on for sure. There have been some games where it wasn't how it was out there today.
"Hopefully we can build on it and put out a similar performance next week and get some points (against Wolves)."
Harwood-Bellis returned to the starting lineup after fully recovering from a small injury that has caused him problems since the turn of the year.
"I've had a little niggle which has been annoying," he explained. "It was something I was carrying for two months and it got to the point where I couldn't play anymore.
"I had to take some time out and it's better now. It's good to be back out there playing for the fans and with the boys. We are trying to get some points."