By Gabriel Tan in Bangkok
The War Elephants sealed their progress to the semi-finals from Group A after a comprehensive triumph at the Rajamangala Stadium, which started in the 20th minute when Teerasil netted with an ingenious strike.
Apipoo Suntornpanavej then doubled Thailand's lead on the hour mark shortly after coming on as a substitute, before Teerasil netted twice more in the final eight minutes to cap off a wonderful night at the office for the hosts.
Speaking after the game, Schafer admitted he was pleased with the contribution from his spearhead and went as far as to claim he was not just one of the best players in the region, but the continent as well.
"He [Teerasil] is one of the best players in Asia," he told ESPNSTAR. "He's fantastic.
"Last year he was very good in qualification [for the 2014 FIFA World Cup], he's played at a fantastic level this year for his club Muangthong United and I'm very happy for him.
"He's definitely one of the best players in Asia; very clever and everybody likes him."
Having singled out left-sided duo Theerathon Bunmathan and Anucha Kitpongsri for praise after the 2-1 win over Philippines last Saturday, the German took the time on Tuesday to show his appreciation for captain Panupong Wongsa.
"The last time I talked about two players - Theerathon and Anucha of Buriram [United] and Chonburi respectively," Schafer added.
"I do not want to forget one player who has been fantastic for us - our captain Panupong. He has shown a good example and contributed in team meetings, and I'm very happy he's playing for us."
Although Teerasil and Panupong were both identifed as key members for Thailand, Schafer did speak highly of the strong team spirit in the camp, which he believes is a key factor in their strong performances as every player is ready to do their part.
Furthermore, he even revealed he would be rewarding some of his charges with a game in their final group outing against Vietnam, especially with one eye on the semi-finals.
"I want to congratulate all my players, including everyone on the bench," he said. "Everybody is very happy and fighting for the common cause.
"There's very good spirit and mentality in this team.
"For our next game against Vietnam, we have three players on a yellow card so they will not play - that's a risk we cannot take.
"We also have some players carrying injuries but our bench is very good. We will play a good team against Vietnam as we want to win.
"I don't like losing matches. I want to win against Vietnam and we cannot take it like a joke and then get knocked out in the next round. We have to always play at the same level."
Myanmar team manager Tim Myint Aung admitted his side were outplayed by Thailand on the night, but is hoping they show better levels of concentration in the future.
"The better team won in today's [Tuesday's] game," he said. "Thailand are a very good team and that's why they won.
"I don't want to blame our players but in three or four positions, they lost their concentration. In every game, if you lose your concentration you won't win.
"We were given a lesson from our opponents but we should accept this result. Thailand were very good technically and tactically."
Given Myanmar's relatively-young side, Myint Aung is hopeful they will learn from the defeat but is hoping they do so by Friday, when they take on Philippines in a must-win game.
"Today [Tuesday] we made a lot of mistakes," he added. "We showed too many weaknesses and now we have to address this for our next match.
"Our defending, attacking and technique was very different from the last match [a 1-1 draw with Vietnam].
"Our team has so many yonug players and they need experience, but they played hard. They gave it their al and I appreciate them.
"We have to learn from this match and we need to beat Philippines."
Myanmar's best performance at the Suzuki Cup came back in 2004 when they reached the semi-finals before being eliminated by eventual champions Singapore.
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