Shami exploited the conditions on offer on the fifth day to the fullest by snaring five wickets while Jadeja bagged four.
Ashwin may have taken just one wicket in the second innings but had picked up seven in the first. In the process, he equalled Sri Lankan spin legend Muttiah Muralitharan to become the fastest to 350 Test wickets in 66 matches.
"Ashwin has a lot of Test cricket experience, and bowled very well in both the first and second innings," Shami said on Star Sports' Cricket Live programme after the match.
"When you have great bowlers like Ashwin and Jadeja in the team, the fast bowlers can breathe easy and relax, knowing that they are there," the pacer said.
Shami also hailed India captain Virat Kohli for giving the bowlers freedom to decide the length of their spells.
"Virat Kohli as a captain always hears us out and gives us the freedom to follow our strategy during the match. He has given us the freedom to take a call on whether we want to bowl 5 overs or 7 overs or more he says 'if you have the power, go ahead and bowl'. That's when we take a call that we will bowl three overs but with full power... That's the understanding we have. He trusts us, and we trust him," Shami said.
( With inputs from IANS )