Snodgrass, 25, was part of the 28-strong group named ahead of the games against Serbia and Wales, which also included Norwich team-mate Russell Martin as well as Brighton midfielder Liam Bridcutt, Dundee United winger Gary Mackay-Steven and Peterborough winger George Boyd as Strachan looks to the future.
Snodgrass believes the former Celtic and Middlesbrough boss will bring a fresh dimension to the Tartan Army.
"He said he watched me in the Liverpool game when we got beat 5-0 which probably wasn't the best, but he was quite happy with my performance which was quite hard to believe because I did not do much in the game," said Snodgrass.
"But he judges people off a 5-0 win or a 5-0 defeat, which tests your character and he was quite happy with that."
Snodgrass added: "He has been bringing different ideas to what we had under previous managers, and is giving a lot of different people a call-up, which is interesting.
"He has different plans, he wants us to press and play football which we have not done over the years. He will try to stress to you the way he wants you to play in that position, to fit into his game plan.
"We have had players come in and out into the set-up, he is now trying to get a balanced squad to play in the positions he wants and I am just happy to be part of that, to try to get some more minutes under my belt to help Scotland."
Scotland may have failed to reach a major international tournament since the 1998 World Cup in France, and are currently bottom of Group A with no wins from their first four matches, a record which ultimately cost Craig Levein his job.
Snodgrass, though, feels there are plenty of reasons to be positive for the long-term progress of the Scottish team, and he added: "There is a lot of expectation because there are some good Scottish players coming through and also playing at a higher level, which is good for the country."