Director of rugby Cockerill said: "The run in the Cup will do a massive amount for confidence in the squad. The spirit will be hugely enhanced by what those lads did in the tournament.
"Players came in and took their opportunity. It's great for all those younger guys and some of those guys on the fringes to be playing and enjoying it, and developing and winning at the same time.
"All those lads who consider themselves as first-choice will be saying 'that is a good win' and it will pick everybody up.
"Guys had opportunities in this competition, they came through and I have nothing but praise for them."
England internationals Manu Tuilagi, Tom Croft, Geoff Parling, Ben Youngs and Dan Cole supported the team from the touchline in the Cup final, and now all five, plus Italian prop Martin Castrogiovanni, are available for the run-in as Tigers chase a place in an eighth consecutive Premiership final.
"It's always about the collective," added Cockerill. "The lads on Test duty will get some stick for not being involved in the final, but it is always all about the club.
"The guys on international duty have being playing well. Now they come back in and that makes us very strong with them and the confidence the rest of the guys have shown in the Six Nations period.
"It has been a hard season for all sorts of reasons, there has been lots of flak coming our way but we kept working and believing in what we do. The attitude of the players has been outstanding. Now we have to make sure we have to get back to the Aviva Premiership and make sure we get it right."
After the trip to London Irish this weekend, Tigers return to home soil on Friday, March 30 for the match against Worcester Warriors. Tickets are available now.