The Taifa Stars started the encounter with their East Africa neighbours brilliantly after Simon Msuwa opened the scoring, six minutes into the game.
Michael Olunga brought the Harambee Stars back into contention with an improvised overhead kick in the 39th minute but captain Mbwana Samata restored Tanzania's lead just before the half time break.
However, the Taifa Stars lost momentum in the second half as Johanna Omolo equalised for Kenya before Michael Olunga sealed the victory with his second goal of the game.
The defeat means Tanzania are eliminated from the competition after also losing their opening game to Senegal.
“The reality is in a game of football if you don’t know how to manage the game to your advantage, you pay for it,” Amuneke told Goal.
“We started on a very good note, scoring first then leading the game towards half time, but there were a lot of crazy things. we committed a lot of mistakes, the second goal, the Kenya equaliser, this is what we have practised over and over, knowing they have dropped the ball in the first place.
“As a coach you are helpless, you feel you want to help them, but you cannot turn it around. Most players play in the Tanzanian league, we lack experience, it’s a good thing we came to this Afcon, and it’s a good thing for Tanzanian football, to open their eyes. The truth is that at the moment we’re not in a position to compete.
“Our target, we are privileged to have qualified for the Afcon, after so many years we’ve missed out and now we’re here after all these years. Every team wants to do well, every team wants to go far, but you could see, we’re still lacking a lot of experience, character, maturity.”
With many of the players plying their trades in the Tanzania League, Amuneke believes his players need to play abroad for exposure and experience to help the national team grow.
“The Tanzania league has two of the best teams in Tanzania - Simba and Yanga - they have 22 teams but the reality is not about the league, the truth is that the players need exposure, they need to play in places where they can grow and compete with the other players in Africa," he continued.
“We’re not being harsh with our players, just realistic. In football, if you are lovers of football, following football, you need a lot of experience, to be in a position to compete, and the reality is that we don’t have the ability to compete with the rest.
“For us, being in the Afcon is an eye-opener for us, a big experience and a big achievement. You can fall in football, but if you believe in it and you stick to it, you can bounce back again. It’s not about how talented you are, players must know what to do when you have the ball, when you don’t have the ball. From the second goal, it was the wrong ball, the wrong moment, and in that second we lost the goal."
Amuneke wants his side, who are making their first appearance in the finals for 39 years, to learn from the mistakes that led to their early exit from the tournament.
“Being here alone can inspire us. No one believed that Tan would qualify, and today we are here. Unfortunately for us we’re not in a position to win our games, but it’s an experience," he added.
“We go back and we look at our players, players we can bring in, players who can help the team. Players who can have some responsibility then you can say you are growing. I always say that what is good today in football is backdated tomorrow. If you never grow, you will never be in a position to correct it.”
Tanzania will face already qualified group leaders Algeria in their final Group C match at the 30 June Stadium on Monday.