Some people think that because the opponents faced by AS Roma were not too strong so De Rossi easily beat them, especially since Hellas Verona has only been able to win four matches in Serie A. But if you look at when playing at home to Hellas Verona, AS Roma suffered defeat while still being coached by Jose Mourinho and this shows that De Rossi had a good start in coaching AS Roma. I see the match against Inter Milan which will be a little more difficult because currently Inter Milan is really strong and difficult for any team in Serie A to beat.
AS Roma with their quality can win or lose against Verona with any coach. De Rossi got a good match with his players and won it but next times, they might lose against Verona. Roma are stronger than Verona, have better quality than Verona but they are not stable in performances and can lose or win unpredictably.
In addition with Roma's limited player resource, one or two player absence can cause a lot of change in their squad quality and perform in a match.
De Rossi has to prove his ability to coach and I think this is an opportunity for him if he wants to become one of the coaches to be taken into account. The match against Inter Milan is quite difficult because currently they are at the top of the standings with a fairly consistent form of play. But nothing is impossible as long as the players have the motivation to beat them and at least De Rossi can provide resistance which ends in a draw in the match which is more than enough.
Have a first match for a club and even a winning, are not enough to prove De Rossi is a good coach. We will need to wait for like 5 or 10 matches to assess the ability of De Rossi. Even with 5 or 10 matches, it will be still too little but at least, better than making assessment on De Rossi ability after only one match.
Roma are in a very crowded competition with 4 or 6 clubs just to get in top four, it will be a tough competition for De Rossi and it is a very big task for a young coach like him.