Chelsea were improved in a spirited first-half display but lacked a cutting edge again, and were made to pay by Rodrygo’s close-range double after the break.
The Blues still have seven League games remaining but are stranded in midtable and would need to dramatically improve to even have a chance of qualifying for the Europa Conference League.
“The motivation [in the run-in] has to be playing for Chelsea,” Lampard said afterwards. “There are some players who are quite new here who are getting used to the club and that isn’t easy. Some of our players there is a bit of transitioning.
“But in terms of motivation, you are playing for Chelsea. We have to be absolutely competitive in what we do every day.
“I picked a team today that I thought was the most in-form team and the fittest team and they showed they can compete with Real Madrid, other than the final third stuff. It is important to take each step.
“People will make a lot of this season for Chelsea because we have had so much success. The reality is this club is going to be back, it will take work and process. But I think the fans appreciated the performance today, and maybe this season they have had moments where they’re not feeling like that. We have to latch onto that, get results at the end of the season and performances and go again next year.”
Lampard insisted his focus is on the run-in but pointed out that Chelsea last won the League in 2016-17 when they were not in Europe.
He added: “We have been fortunate enough to have huge success for 20 years.
“Many clubs in the Premier League would only dream of our success as Champions League and Premier League winners.
“Maybe this is a year where we are not what we wanted to be, there are reasons for the transition. A few years ago Chelsea we didn’t make the Champions League and then won the Premier league the following year [in 2016-17]. We can’t be too short term with it. There are places we want to improve as a club.
“I don’t think it’s time to jump too far ahead. The step in front of us is seven games in the Premier League to show that performance because that’s the standard. The end bit being clinical and scoring is absolutely crucial and something we need to address.”
Lampard was frustrated at the amount of stoppage-time added by the officials on the night and said Real centre-half Eder Militao should have been sent off for catching Trevoh Chalobah at 0-0, having earlier been booked for a rash tackle on Kai Havertz.
“It is for the officials to be aware of [the amount of stoppage-time],” he said.
“It is a high level game, two minutes in the first half wasn’t enough for me but I don’t want to complain about that after the result.
“But Militao for me was a second yellow card, I won’t say what I really think but at this level, that one in the attacking final third when our player is beyond their centre-back and gets brought down, normally that’s a yellow card. Which means red, which means half an hour of what we had to do at the Bernabeu [play with 10 men].
“We thought they would have had to do it here but it didn’t happen.”