Goals from Alan Connell and Peter Bore secured a 2-1 win over the League One side.
"Nobody is getting carried away with the win but winning is a lovely habit to get into," Woods told the Grimsby Telegraph.
"We know that wasn't Sheffield Wednesday's first side and was mixed up but they still had good players.
"The most pleasing thing for me was the attitude of my players. We played some good football at times and had a little bit of everything."
The Mariners will spend this week at a training camp in Scotland. The first-team squad will be based at Stirling University, and play a friendly against Stirling Albion on Tuesday evening.