Clermont had a 16-point lead before No8 Crane scored from a clever break by Jamie Gibson and Blaine Scully following an Owen Williams cross-kick.
“That try gave us a lifeline just before half-time,” said Slater after the 22-16 defeat at the Stade Marcel Michelin.
“It was a massive boost for us after the way they had started the game.
“They are a very strong side at home, with the crowd behind them, and it was tough. It felt like they were scoring every time they got into our 22 but we managed to claw our way back in difficult circumstances.
“We had spent a lot of time defending in the first half and at half-time we just said we had to go back to the basics of the gameplan and keep hold of the ball.
“Owen Williams carried on where he left off at Northampton last week with his kicking, and that penalty early in the second half was huge for us in terms of gaining some momentum. That was important.”
A third Williams penalty brought the score back to 19-16 as Tigers chipped away at the Clermont lead.
“We showed great character to come back against a very good side,” said Slater. “To get within a score at the end is a credit to the boys.”
Slater and the team return to Welford Road on Saturday for the visit of London Wasps in the Aviva Premiership. Kick-off is at 3pm and this game is not being shown on live television. Tickets are available now from the Tigers ticket office. Phone 0844 856 1880 or visit Welford Road to secure your tickets. Or click here to book online.