Strachan said: "It was a good day at the office. The result and the performance gave us the chance to rest two or three players at the end of the game. There was a bit of pressure on us because three points would have taken us top.
"But it's always nice to know that you can go top of the league, the other side of it is, if you don't make it then it would have been a downer for us going to Donetsk.
"But we are doing fine. It's the best start to the season since I've been here so it's not too bad."
Caley remain rooted to the bottom of the table with no points after six games.
However, Strachan praised the visitors who were hampered not only by some slack defending but by poor finishing which allowed the champions a relatively easy afternoon.
He said: "What surprised us was the enterprise that Inverness showed.
"For a team that was bottom of league, they had their central midfielders trying to break beyond their forwards which threw our central midfield players for a while.
"I thought they had a smashing game."
The Highlanders' player-manager Craig Brewster explained his decision to drop himself from the squad then declared that he is not worried by his side's dreadful start to the season.
He said: "I felt Dennis Wyness was doing well so I decided to put him in - it was the manager's decision. I have total confidence in the team.
"I don't know many teams who come to Celtic Park, play the way we did and create as many chances as we did against the champions."
