It looked as though Robin van Persie's first-half goal had handed the champions all three points, but Adam Lallana's 89th-minute equaliser ensured that the Saints left Old Traffrod with a share of the spoils.
"We started the game very well, and the first 20 minutes was very strong - we controlled the game," Fonte told BBC Radio 5Live. "After that we went to sleep a little bit and they scored, but we managed to stay in the game and had a good team talk at half time.
"The gaffer told us to believe in ourselves and our philosophy. In the second half we came back and kept going, kept pressing. We dominated the second half and deserved the equaliser.
"We deserved at least a point. The whole team works very hard as a team, and the results are there to see. We need to keep going, keep working and keep improving."
Fonte has been an ever-present figure for Southampton this season.