Both sides scored three tries, with Tigers taking an early lead but then having to come back from a 10-point deficit in the last quarter to finally rescue a draw with a last-minute try from Jamie Gibson.
“It was a good contest all over the pitch, with two good sides having a crack,” said Tigers director of rugby Cockerill.
“It was a good game with both sides wanting to play, and it ebbed and flowed for the full 80 minutes.
“We’ve probably both got mixed feelings afterwards but we’ll take the two points and move on.”
A Miles Benjamin try gave Tigers an early platform but then Bath scored three tries to lead 27-17 before tries from replacement Thomas Waldrom and fellow back-rower Gibson completed the scoring. Owen Williams had an opportunity to win the game with a touchline conversion but saw the ball drift wide as honours ended even.
“Never question the character and resolve in our players,” said Cockerill. “At 10 points down they were still playing to get back into the game and they did that.
“We made some errors in defence but Bath are a good side and have players in that backline who can expose those errors and they did that really well. They took their opportunities very well.
“Bath have been good all season and played well again. But we battled hard and scored three good tries, and we got ourselves into a position where we could have won it with the last kick which is a credit to all the players.
“A win would have put us into the top four but we are there or thereabouts with 10 games to go, level on points with fourth place. We’re still in with a shout in Europe and in the mix in the Aviva Premiership. We have got to be pretty positive about where we are.
“The season is alive and with the players we have still to come back in we have got to be positive.”
Tigers return to European duties for the next two weeks, with a trip to Benetton Treviso this weekend followed by a home game against Ulster on Saturday, January 18 (6pm kick-off).