The midfielder has heaped praise on his team for their comeback against Southampton which saw the Merseyside team win 3-1 at Goodison Park after falling behind to a Ramirez opener
The Englishman insists the character of the squad helped their comeback, triggered by Osman's opportunistic equaliser and 45th goal for the club.
Osman told evertontv: "No one wants to start the game by going a goal down in the first few minutes, but we showed good character.
"The lads didn't panic and didn't get nervous. We carried on playing and were rewarded with the goals before half time."
David Moyes' side are enjoying a fine start to their campaign and although they were humbled by Leeds United in the League Cup in midweek, they currently sit second in the Premier League after four wins from their opening six games.
Osman pounced on a loose ball in the box before smashing it into the roof of the net - a strike that was inches away from missing the target.
"It probably went a little bit higher than I was going for," he admitted. "But it went in and that was the pleasing thing.
"We're playing some decent football at the minute. Hopefully the fans are enjoying it because we are.
"But we've got to make sure we score the goals when the opportunities come and we did that on Saturday."