"We lacked football intelligence in key moments of the game and that cost us," Constantine said after the match.
India came into the game on a the back of a similar result last week against Oman, who though faced stiff competition form the South Asian nation.
Sunil Chhetri managed a consolation goal in the last minute of the game after Brandon McDonald put the hosts ahead in the 38th minute and Travis Nicklaw doubled the advantage in the 62nd minute at the GFA National Training Center.
Ranked 174 in the world to India's 141, this was only their second World Cup qualifying win, the result coming less than a week after Guam's 1-0 victory over Turkmenistan in Group D.
Constantine, however, dismissed that jet lag was ever a factor.
"We have been here for three days. This is international football and you have to deal with it. The time zone was not a factor at all.
Constantine's counterpart Gary White sounded happy with six points on board.
"From the very outset, we knew that this would be a difficult place for anybody to come. It was a tough and competitive game and it feels nice to be at the top of the Group. This is not the same Guam who used to play some 15-16 years back," White said.
