Saturday's Twickenham showpiece will be followed the following weekend by the Heineken Cup final against Wasps at the same venue.
"We're very proud we've done something which is pretty big but you come into these one-off finals and we've got to make sure we finish the job," Howard said after masterminding Saturday's 26-14 play-off semi-final win over Bristol.
"We know we've got two very hard teams to play, we'll have to play them back to back.
"We've also had a lot of hard games on the trot, a lot of blokes came off the back of the Six Nations, so it's been a intense period and the players deserve an immense amount of credit and respect."
As well as looking to complete the second leg of the treble, Leicester will be competing in their third straight Premiership final on Saturday, having finished runners-up in the last two years.
Howard, who will return to his native Australia at the end of the season to run a pharmaceutical business, is refusing to contemplate a hat-trick of defeats, saying: "That's a part of history, that's done, that's finished."
He pointed out his side had already tasted Twickenham success this season, in the recent EDF Energy Cup final.
"We've already been to Twickenham this year and won," he said.
"We've played in some big games, some pretty big one-off games and we've dealt with that so I think there's a line under that.
"We're very keen to go back to Twickenham two weeks on the trot."
Howard's men were given a severe physical examination by long-time league leaders Bristol, with Harry Ellis suffering a knee injury that could rule him out for one or both of their final two matches.
There were also other bumps and bruises but Howard insists he has the squad to cope with such injuries.
He said: "I've done a lot of rotation in the Premiership all year and if someone has to step in, he's probably played 10 or 12 games.
"If that happens to be a Premiership final, then fantastic for him, a great showpiece for him to stand up in."
Saturday's game may have been Howard's Welford Road farewell but it was watched by the ground's lowest crowd of the season, 10,675.