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GB, who drew with Australia in their first game on Friday, were two down before the midfielder consolation.
Britain need to realistically win all of their remaining three pool fixtures to reach the 17 June final.
"We dominated and had our chances but didn't even take shots at times and it was terrible really," Jackson said.
"We weren't very good against Australia last night, but we ground out and got a point - today we were just lacking real quality and it's fairly embarrassing," he told BBC Sport.
Mandeep Singh gave India - the lowest ranked team in the competition - the lead in the second quarter after a swift counter attack, before Harmanpreet Singh doubled their advantage with a penalty stroke.
Jackson struck in the third period but despite late pressure GB were unable to find an equaliser.
"One of the things that's frustrating for us is that we did create the chances but didn't actually manage to convert them into corners and goals," forward Simon Mantell told BBC Sport.
"There's definitely frustration in there for us and a lot to go away and think about because we need to build up our performance throughout the competition."
In the day's other fixtures world number one side Australia beat South Korea 4-2, whilst Germany salvaged their second late draw of the event in a dramatic 4-4 encounter with Belgium.
After each of the six teams have played each other in the initial 'pool' stage, the top two ranked nations will compete for gold - with third and fourth facing off for bronze.
Great Britain's men next face South Korea on Monday.
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Great Britain's 2-1 Champions Trophy defeat by India at London's Olympic Park was described as "embarrassing" by goalscorer Ashley Jackson.