Warren Gatland claimed "it could be embarrassing" if Wales replicate their performance against Italy when they face England in a fortnight's time.
Wales backed up a Guinness Six Nations victory over France by defeating the Azzurri 26-15 in Rome thanks to second-half tries by wing Josh Adams and centre Owen Watkin.
Wales equalled the longest unbeaten run in their 138-year Test match history, making it 11 successive victories and matching the sequence set between 1907 and 1910.
But it was a stop-start performance by a Wales team showing 10 changes from the one that triumphed in Paris eight days ago.
"There are lots of things we need to improve for England," Wales head coach Gatland told ITV.
"We all need to improve in lots of areas to beat England. They are a pretty good side at the moment.
"If we play like that against England it could be embarrassing."
Speaking at his post-match press conference, Gatland added: "It wasn't a great performance, but sometimes you have to win ugly.
"We didn't play that well, but as I said to the boys in the changing room, we will take the win, move on and start thinking about England."
Asked if he regretted making wholesale changes, Gatland said: "I don't regret anything. I was looking at the bigger picture.
"For us as coaches, in our last year, we want to have as good a World Cup as we can. That was the plan all along. There is no regret.
"We are two (wins) from two, and we have a couple of weeks of training before England. It sets us up nicely for the England match.
"A lot of people will be writing us off, which is a good position to be in. Hopefully, we will go under the radar, have two good weeks of training and get ourselves mentally and physically right.
"We didn't play as well as we would have liked.
"Probably part of that is that we didn't have the continuity that we would have if we hadn't made so many changes.
"We didn't really get out of jail. I don't think it ever looked like we were going to lose the game, but we weren't as accurate as we could have been.
"You are not always brilliant, and we weren't today. We will be a lot better against England.
"We didn't speak about the record (11 wins) at all this week, but we will probably talk about it before England.
"If this group of players achieve that, it will be something nobody can take away from them. There will definitely be no lack of motivation in trying to beat England and break that record."
During the game, the radio link between referee Mathieu Raynal and the television match official appeared not to work in an embarrassing episode for Six Nations chiefs, and when Raynal had to rule on try-scoring moments, a set of headphones were brought on for him to communicate with the TMO.
Wales skipper Jonathan Davies said: "I think there was a breakdown in communication with a technical fault.
"There is always a lot to talk about with things like that. It didn't affect the result of the game, thankfully."
Fly-half Dan Biggar kicked 14 points and Gareth Anscombe converted Watkin's touchdown, but Italy, despite slipping to a 19th successive Six Nations defeat and a 13th on the bounce against Wales, battled hard throughout.
They claimed a first-half try from flanker Abraham Steyn, with fly-half Tommaso Allan kicking a penalty and conversion, before wing Edoardo Padovani crossed late on.
Reflecting on the result, Italy boss Conor O'Shea said: "I am really disappointed.
"I see a group in our changing room that are so driven and have a desire to succeed.
"They know the scale of the challenge, but we will just dust ourselves down."
