Mourinho guided Roma to back-to-back European finals, winning the Europa Conference League in 2022 and losing to Sevilla in the Europa League final earlier this year, but with the club 16th in Serie A, the pressure is now on.
Following the heavy loss to Genoa, he reminded the press of those achievements.
"It's also my worst start to a season as a coach," he said when told it Roma's worst-ever start to a campaign.
"However I don't think that Roma had ever appeared in two consecutive European finals (before last season).
Roma have just one win from their six league matches so far and a growing injury list is not aiding Mourinho's cause, particularly in defence.
"When we're missing certain players, we lack solidity," he said.
"However, to state that our weakening solidity is the result of the absence of this or that player wouldn't be correct. Our lack of defensive stability is down to the team as a whole - what happens when we lose possession and when we drop deeper."
With Roma back in action against Frosinone on Sunday before a Europa League fixture against Swiss side Servette on October 5, Mourinho said there is no point in stewing over their problems.
"This is the squad we have, for better and worse. We have to move forward – there's no time to lament," he added.
"I might show my feelings behind the scenes because it really affects me emotionally, especially given my relationship with the fans.
"We'll be working hard from tomorrow ahead of our next game. Three points will be at stake – it's not like we're in six-pointer territory already – but it's a huge game for us now."