The attacking midfielder scored and provided an assist for the Reds but they were denied qualification for the knock-out stages courtesy of a late leveller from the visitors
Udinese's 2-0 defeat to Anzhi Makhachkala earlier in the day meant the Reds could have sealed progress to the last 32 of the Europa League with a victory at Anfield.
However, a last-gasp wonder-strike from Elsad Zverotic secured a share of the points for the visitors, and left Cole rueing the Merseyside outfit's inability to close the game out.
"It’s disappointing not to get the right result," he told reporters. "We could have managed the game better but we need to learn from these experiences so that, when we’re in this situation again, collectively we can do a lot better.
"Overall it’s a feeling of ‘we could have done better’. A lot of positives come out of the game, [it’s] another game for the young lads but we need to move on.
"It was an enjoyable game to play in but the result wasn’t great so we’re disappointed we didn’t come away with a win to see us through."
The 31-year-old went on reveal that he volunteered himself for substitution with 75 minutes played as a result of tightness in his hamstring.
However, he remained adamant that the problem will not rule him out of Sunday's clash with Swansea and expressed confidence that he can flourish after an injury-hit start to the season.
"My hamstring was a bit tight. It’s the longest I’ve played in that position and I got through a lot of running but I don’t think it’ll be anything sore and I’ll be available for Sunday," he continued.
"It was nice to be out there playing. It’s my third game back and I’ve felt stronger in every game I’ve played.
"I’ll keep plugging away, it’s just football. I’ve been a good player at West Ham, Chelsea, Lille and [for] England when I’ve played, so I’m sure if I play football here I’ll be a good player for Liverpool."
The Merseyside club will travel to face Udinese next needing to both avoid defeat and match Young Boys' result against Anzhi to ensure progression, and Cole is determined to help make that a reality.
"[Qualification] is very complicated, we’re trying to work it out," he added.
"[We want to] win the game, that puts it all to bed. It’ll be tough out there but maybe we’ll go there strong.
"Liverpool need to be playing European football after Christmas so we’ll go there strong and try and win the game."