The Tigers currently sit in fifth place in the Aviva Premiership standings, with 51 points from 18 games played.
They are three points behind fourth-placed Newcastle and will need to keep up the momentum right to the end of the campaign if they are to be involved in the post-season.
May is in his first season at Welford Road, having moved from Gloucester last summer, and is now back in the ranks following his involvement in the Six Nations with England.
The 27-year-old knows it will not be easy but is banking on the Tigers putting it all together when it matters.
"Every week is hard. We have a reasonable run-in but we will take it one week at a time for sure and respect every team that we play," he said.
"I think every team in this league has had a tough spell this season. We have come out of it in a better place but we need to finish strong. I'm sure we will.
"I've not been a part of it in this environment so far but I've always seen Tigers finish strong and I'm sure we'll do the same this year."