After leading 2-0 at half-time, third-placed Lazio were pegged back as Inter salvaged a 2-2 draw at San Siro in Milan.
Lazio stormed out of the blocks thanks to in-form Brazilian striker Felipe Anderson, who scored twice in the first half.
But the visitors had no response to a rejuvenated Inter - 11th in the standings - with Croatian sensation Mateo Kovacic inspiring a comeback.
Kovacic unleashed a thunderous volley from the edge of the area in the 66th minute before Rodrigo Palacio equalised 10 minutes from time.
Speaking post-game, Lazio boss Pioli said it was not a case of the capital club switching off, but Inter lifting their intensity in the second half as a result of Kovacic's strike.
"It's not that our light went out, more that Inter pushed very hard," Pioli told Sky Sport Italia.
"It's a shame, as we should've kept the ball more and controlled possession, but Inter were extremely aggressive.
"Kovacic scored that fantastic goal and it boosted their morale, so we were pegged back even more. The team fought for the whole game, but we should've slowed the tempo and kept the ball better.
"Obviously winning 2-0 at half-time we wanted to win, but we misplaced a few passes, poor clearances and were unable to get the victory.
"Kovacic's fantastic goal really changed the game, as they have such quality and it got their tails up, giving them hope.
"We were playing at San Siro against an Inter side that was determined not to lose again. We go home with a positive result after another good performance."
