The Norwegian was propelled into the job on a caretaker basis last December following Jose Mourinho's sacking and won 14 of his first 17 matches in charge.
But United's form turned after he was handed the top job on a permanent basis as they ended the 2018-19 campaign with one win in nine matches, leading to some questioning the decision to hand him the role full-time.
Ahead of Chelsea's opening-weekend trip to Old Trafford, however, Lampard insisted the criticism Solskjaer has faced is not justified.
"I am aware of it and it comes with the territory," he said at his pre-match news conference. "It can be excessive, for everyone in football. I think it is possibly harsh as it is something that he came in to.
"You have to look at him this season and what he gets to do. I don't listen too much to things."
Like United, Chelsea have been written off for the title by many before a ball has been kicked this season after losing star player Eden Hazard to Real Madrid.
But Lampard, whose job has been hindered by Chelsea's two-window transfer ban, was relishing the prospect of silencing his side's critics - starting with victory at United on Sunday.
"I love hearing predictions when we're not in the top four and there isn't anything better than proving people wrong," he said.
"I love playing at Old Trafford. It is a big game for both teams. We are both huge clubs that have had a lot of success.
"We both have the same idea that we want to be successful. We want to be competing."
09/08 - On this day in 1997, Frank Lampard scored his first ever Premier League goal, for West Ham against Barnsley. Lampard is the highest scoring midfielder in PL history (177). Icon. pic.twitter.com/uXMsaRGHKG— OptaJoe (@OptaJoe) August 9, 2019
"Manchester City and Liverpool showed there was a gap, everyone has to make it up," he said. "We will aim to win and of course we want to be in the Champions League every year. We are realistic and we just have to work our hardest.
"The gap [is bridgeable] because this is football. One of the beauties is that you start again fresh."
Lampard also confirmed he will make a late decision on whether to use fitness doubts N'Golo Kante, Willian and Antonio Rudiger at Old Trafford.