Presnel Kimpembe and Kylian Mbappe scored in the second half as PSG overcame the absences of Edinson Cavani and Neymar to triumph at Old Trafford.
The reverse was United's heaviest at home in European competition, while no side in the history of the Champions League has ever progressed from a knockout tie having lost the home first leg by two or more goals.
But Herrera pointed to their recent run of good form as a reason to remain optimistic.
United have recorded away wins over Tottenham and Arsenal - beating the latter in the FA Cup - under Ole Gunnar Solskjaer, though Tuesday's result was the Norwegian's first defeat since taking over on an interim basis.
"I think the game was tight until the corner [from which Kimpembe scored]. After the first goal they played the way they wanted," Herrera told BT Sport after a testing evening for United which also saw Paul Pogba sent off late on.
"After the first goal everything changes, it was under control and we were better until that moment. The game could have finished 0-0 if they hadn't scored from that corner, but they did.
"After that they played on the counter, they have very quick players, but it was tight until the corner.
"Now we have good examples, having won at Spurs and Arsenal - big teams, big games, and we will try to win away. We all are very optimistic and positive, it's just one result and we're in a good moment. We're going to continue.
"It's a tough night and tomorrow will be a tough day but our focus is to stay in the top four and stay in the FA Cup."
United are next in action in the FA Cup on Monday, as they visit Chelsea in the fifth round of the competition.
They then have Premier League meetings with Liverpool, Crystal Palace and Southampton to take in before travelling to France for the second leg of their last-16 encounter with PSG on March 6.