Tigers, back in action for the first time in three weeks, claimed tries from Jeremy Staunton, Ben Youngs and James Grindal, with Toby Flood kicking 24 points to stay top of the Guinness Premiership table.
The defending champions now have just four games remaining, though the chasing pack have a game in hand.
“There is still a way to go, but we took another step in the right direction today,” said Cockerill at the final whistle.
“We told the players in midweek that some people may be talking about us having a home semi-final already, but that is not the case if you lose a game and the other teams win their game in hand.
“It was a good win, especially as we have found it pretty tough at Worcester over the years, and now our focus is entirely on Bath at Welford Road next Saturday.”
Tigers led 13-12 at half-time, and Flood kept the scoreboard ticking over with four second-half penalties to go with the scores by scrum-half Youngs and his late replacement Grindal.
“We were a little bit rusty at times,” said Cockerill. “Having a couple of weeks off at this stage of the season is new to us, but I’m pretty happy with the performance against a team that is battling for everything. It is a good win for us.
“We made a few mistakes but we rode the storm then controlled the game and the field position in the second half.”
Cockerill was forced into making late changes to his line-up, with Geordan Murphy and Martin Castrogiovanni failing late fitness tests. But neither is expected to be sidelined for long.
“They should both be back okay for next week, as well as Louis Deacon who came back injured from the Six Nations,” he said. “Hopefully we’re heading into the run-in with a pretty full squad.”
Tigers host Bath as part of a rugby double header at Welford Road on Saturday, with the Guinness Premiership showdown at 3pm followed by a match between Tigers Academy and England Under-20s. Tickets are available now, book early to guarantee the best available seats.
Phone the Tigers ticket hotline on 0844 856 1880, book online or call in at Welford Road. Special rates are available for Group Bookings and you can make it a great Easter day out by buying a family ticket (2 adults and 2 children) which entitles a second child to free admission.