Adebayor had been frozen out of the squad under former Spurs boss Andre Villas-Boas, but has been brought back into the fray since Sherwood took over in December.
The Togo striker has scored 11 goals in 15 outings, including two a 3-1 win over Dnipro in the Europa League last-32 Thursday, goals which helped send the Londoners through 3-2 on aggregate.
"I'm playing well for my team and I'm happy for my team," he told ITV. "I just have to keep playing well. I have to say big thank you for Tim for giving me a stage to play on. We just have to keep focused."
Spurs went 1-0 down on the night, meaning they needed three goals in 42 minutes to progress to the next round.
Christian Eriksen pulled one back and Adebayor struck a brace to set up a last-16 tie with Benfica, and the former Arsenal and Manchester City man was never afraid the match was beyond them.
"No, not at all," he added. "I know we have quality up front and on the bench. We knew it would be very difficult because they have an advantage after leading 1-0.
"We just kept our focus very well. When Eriksen scored that goal it put us on the way. We went through so we're very happy."