The 43-year-old was content with the 1-0 win over Mixu Paatelainen's men, whilst goalscorer Abou Diaby was delighted to return to the national team set-up
Abou Diaby struck the game's winning goal after 20 minutes, following a dazzling assist from Karim Benzema. The visitors, however, were lethargic in the second half, with Finland goalkeeper Lukas Hradecky pulling out numerous saves to deny the 1998 world champions.
The 43-year-old remained content with the victory in a group which also contains holders Spain, but insists that the result was never safe.
"In general, we did not start well. We had opportunities in the second half, but there were two beautiful saves from the Finnish goalkeeper" Deschamps was quoted as saying by M6.
"It's a shame. In the end, there were dangerous situations. [When] we do not score the second goal, [the result] is never safe. [However] it is good to win."
Goalscorer Diaby, whose goal proved the difference, instead expressed his delight at the victory, having made his first start for les Bleus since the Euro 2012 qualifier against Belarus in June 2011.
"I am happy to be back. The match ended with a victory, it's a big satisfaction," said the Arsenal midfielder.
"The key is to give the best of yourself in every game."
Following on from the victory, Deschamps' men return to Paris to face Belarus on Tuesday. Kick-off at the Stade de France is at 21:00 CET.